@article {feynman50,
    AUTHOR = {Feynman, Richard P.},
     TITLE = {Mathematical formulation of the quantum theory of
              electromagnetic interaction},
   JOURNAL = {Phys. Rev.},
  FJOURNAL = {Physical Review. Series II},
    VOLUME = {80},
      YEAR = {1950},
     PAGES = {440--457},
       DOI = {10.1103/PhysRev.80.440},
       URL = {https://doi.org/10.1103/PhysRev.80.440},
}

@article {feynman51,
    AUTHOR = {Feynman, Richard P.},
     TITLE = {An operator calculus having applications in quantum
              electrodynamics},
   JOURNAL = {Phys. Rev.},
  FJOURNAL = {Physical Review. Series II},
    VOLUME = {84},
      YEAR = {1951},
     PAGES = {108--128},
       DOI = {10.1103/PhysRev.84.108},
       URL = {https://doi.org/10.1103/PhysRev.84.108},
}

@article {berkos1,
    AUTHOR = {Bern, Zvi and Kosower, David A.},
     TITLE = {Efficient calculation of one-loop {QCD} amplitudes},
   JOURNAL = {Phys. Rev. Lett.},
  FJOURNAL = {Physical Review Letters},
    VOLUME = {66},
      YEAR = {1991},
    NUMBER = {13},
     PAGES = {1669--1672},
       DOI = {10.1103/PhysRevLett.66.1669},
       URL = {https://doi.org/10.1103/PhysRevLett.66.1669},
}

@article {berkos2,
    AUTHOR = {Bern, Zvi and Kosower, David A.},
     TITLE = {The computation of loop amplitudes in gauge theories},
   JOURNAL = {Nuclear Phys.~B},
  FJOURNAL = {Nuclear Physics. B. Theoretical, Phenomenological, and
              Experimental High Energy Physics. Quantum Field Theory and
              Statistical Systems},
    VOLUME = {379},
      YEAR = {1992},
    NUMBER = {3},
     PAGES = {451--561},
       DOI = {10.1016/0550-3213(92)90134-W},
       URL = {https://doi.org/10.1016/0550-3213(92)90134-W},
}

@article {strassler1,
    AUTHOR = {Strassler, Matthew J.},
     TITLE = {Field theory without {F}eynman diagrams: one-loop effective
              actions},
   JOURNAL = {Nuclear Phys.~B},
  FJOURNAL = {Nuclear Physics. B. Theoretical, Phenomenological, and
              Experimental High Energy Physics. Quantum Field Theory and
              Statistical Systems},
    VOLUME = {385},
      YEAR = {1992},
    NUMBER = {1-2},
     PAGES = {145--184},
       DOI = {10.1016/0550-3213(92)90098-V},
       URL = {https://doi.org/10.1016/0550-3213(92)90098-V},
    EPRINT = {hep-ph/9205205},
}

@mics {strassler2,
    AUTHOR = {Strassler, Matthew J.},
     TITLE = {Field theory without {F}eynman diagrams: a demonstration using actions induced by heavy particles},
      NOTE = {SLAC-PUB-5978, 1992, 65~pages, unpublished},
}

@article {41,
    AUTHOR = {Schubert, Christian},
     TITLE = {Perturbative quantum field theory in the string-inspired
              formalism},
   JOURNAL = {Phys. Rep.},
  FJOURNAL = {Physics Reports. A Review Section of Physics Letters},
    VOLUME = {355},
      YEAR = {2001},
    NUMBER = {2-3},
     PAGES = {73--234},
       DOI = {10.1016/S0370-1573(01)00013-8},
       URL = {https://doi.org/10.1016/S0370-1573(01)00013-8},
    EPRINT = {hep-th/0101036},
}

@mics {126,
    AUTHOR = {Edwards, James P. and Schubert, Christian},
     TITLE = {Quantum mechanical path integrals in the first quantised approach to quantum field theory},
    EPRINT = {1912.10004},
}

@article {25,
    AUTHOR = {Fliegner, D. and Haberl, P. and Schmidt, M. G. and Schubert, C.},
     TITLE = {The higher derivative expansion of the effective action by the string inspired method,~{II}},
   JOURNAL = {Ann. Physics},
  FJOURNAL = {Annals of Physics},
    VOLUME = {264},
      YEAR = {1998},
    NUMBER = {1},
     PAGES = {51--74},
       DOI = {10.1006/aphy.1997.5778},
       URL = {https://doi.org/10.1006/aphy.1997.5778},
    EPRINT = {hep-th/9707189},
}

@article {sascza,
    AUTHOR = {Strassler, Matthew J.},
     TITLE = {Two-loop {Y}ang--{M}ills theory in the world-line formalism and an {E}uler--{H}eisenberg type action},
   JOURNAL = {Nuclear Phys.~B},
  FJOURNAL = {Nuclear Physics. B. Theoretical, Phenomenological, and
              Experimental High Energy Physics. Quantum Field Theory and
              Statistical Systems},
    VOLUME = {579},
      YEAR = {2000},
    NUMBER = {1-2},
     PAGES = {492--524},
       DOI = {10.1016/S0550-3213(00)00220-0},
       URL = {https://doi.org/10.1016/S0550-3213(00)00220-0},
    EPRINT = {hep-th/0003070},
}

@article {105,
    AUTHOR = {Ahmadiniaz, Naser and Schubert, Christian},
     TITLE = {{QCD} gluon vertices from the string-inspired formalism},
   JOURNAL = {Internat.~J. Modern Phys.~E},
  FJOURNAL = {International Journal of Modern Physics A. Particles and
              Fields. Gravitation. Cosmology},
    VOLUME = {26},
      YEAR = {2016},
    NUMBER = {7},
     PAGES = {1642004, 20~pages},
       DOI = {10.1142/S0218301316420040},
       URL = {https://doi.org/10.1142/S0218301316420040},
    EPRINT = {1811.10780},
}

@article {Mueller:2019qqj,
    AUTHOR = {Mueller, Niklas and Tarasov, Andrey and Venugopalan, Raju},
     TITLE = {Deeply inelastic scattering structure functions on a hybrid
              quantum computer},
   JOURNAL = {Phys. Rev.~D},
  FJOURNAL = {Physical Review D},
    VOLUME = {102},
      YEAR = {2020},
    NUMBER = {1},
     PAGES = {016007, 15~pages},
       DOI = {10.1103/PhysRevD.102.016007},
       URL = {https://doi.org/10.1103/PhysRevD.102.016007},
    EPRINT = {1908.07051},
}

@article {tarven,
    AUTHOR = {Tarasov, Andrey and Venugopalan, Raju},
     TITLE = {Structure functions at small $x$ from world-lines: unpolarized distributions},
   JOURNAL = {Phys. Rev.~D},
  FJOURNAL = {Physical Review D},
    VOLUME = {100},
      YEAR = {2019},
    NUMBER = {5},
     PAGES = {054007, 27~pages},
       DOI = {10.1103/PhysRevD.100.054007},
       URL = {https://doi.org/10.1103/PhysRevD.100.054007},
    EPRINT = {1903.11624},
}

@article {12,
    AUTHOR = {Mondrag\'on, Myriam and Nellen, Lukas and Schmidt, Michael G. and Schubert, Christian},
     TITLE = {Yukawa couplings for the spinning particle and the world-line formalism},
   JOURNAL = {Phys. Lett.~B},
  FJOURNAL = {Physics Letters. B. Particle Physics, Nuclear Physics and
              Cosmology},
    VOLUME = {351},
      YEAR = {1995},
    NUMBER = {1-3},
     PAGES = {200--205},
       DOI = {10.1016/0370-2693(95)00337-K},
       URL = {https://doi.org/10.1016/0370-2693(95)00337-K},
    EPRINT = {hep-th/9502125},
}

@article {16,
    AUTHOR = {Mondrag\'on, Myriam and Nellen, Lukas and Schmidt, Michael G. and Schubert, Christian},
     TITLE = {Axial couplings on the world-line},
   JOURNAL = {Phys. Lett.~B},
  FJOURNAL = {Physics Letters. B. Particle Physics, Nuclear Physics and
              Cosmology},
    VOLUME = {366},
      YEAR = {1996},
    NUMBER = {1-4},
     PAGES = {212--219},
       DOI = {10.1016/0370-2693(95)01392-X},
       URL = {https://doi.org/10.1016/0370-2693(95)01392-X},
    EPRINT = {hep-th/9510036},
}

@article {dhogag1,
    AUTHOR = {D'Hoker, Eric and Gagn\'e, Darius G.},
     TITLE = {Worldline path integrals for fermions with scalar,
              pseudoscalar and vector couplings},
   JOURNAL = {Nuclear Phys.~B},
  FJOURNAL = {Nuclear Physics. B. Theoretical, Phenomenological, and
              Experimental High Energy Physics. Quantum Field Theory and
              Statistical Systems},
    VOLUME = {467},
      YEAR = {1996},
    NUMBER = {1-2},
     PAGES = {272--296},
       DOI = {10.1016/0550-3213(96)00125-3},
       URL = {https://doi.org/10.1016/0550-3213(96)00125-3},
    EPRINT = {hep-th/9508131},
}

@article {dhogag2,
    AUTHOR = {D'Hoker, Eric and Gagn\'e, Darius G.},
     TITLE = {Worldline path integrals for fermions with general couplings},
   JOURNAL = {Nuclear Phys.~B},
  FJOURNAL = {Nuclear Physics. B. Theoretical, Phenomenological, and
              Experimental High Energy Physics. Quantum Field Theory and
              Statistical Systems},
    VOLUME = {467},
      YEAR = {1996},
    NUMBER = {1-2},
     PAGES = {297--312},
       DOI = {10.1016/0550-3213(96)00126-5},
       URL = {https://doi.org/10.1016/0550-3213(96)00126-5},
    EPRINT = {hep-th/9512080},
}

@article {29,
    AUTHOR = {McKeon, D. G. C. and Schubert, Christian},
     TITLE = {A new approach to axial vector model calculations},
   JOURNAL = {Phys. Lett.~B},
  FJOURNAL = {Physics Letters. B. Particle Physics, Nuclear Physics and
              Cosmology},
    VOLUME = {440},
      YEAR = {1998},
    NUMBER = {1-2},
     PAGES = {101--107},
       DOI = {10.1016/S0370-2693(98)01074-0},
       URL = {https://doi.org/10.1016/S0370-2693(98)01074-0},
    EPRINT = {hep-th/9807072},
}

@article {bastianelli,
    AUTHOR = {Bastianelli, Fiorenzo},
     TITLE = {The path integral for a particle in curved spaces and {W}eyl
              anomalies},
   JOURNAL = {Nuclear Phys.~B},
  FJOURNAL = {Nuclear Physics. B. Theoretical, Phenomenological, and
              Experimental High Energy Physics. Quantum Field Theory and
              Statistical Systems},
    VOLUME = {376},
      YEAR = {1992},
    NUMBER = {1},
     PAGES = {113--126},
       DOI = {10.1016/0550-3213(92)90070-R},
       URL = {https://doi.org/10.1016/0550-3213(92)90070-R},
    EPRINT = {hep-th/9112035},
}

@article {bpsv:npb446,
    AUTHOR = {de Boer, Jan and Peeters, Bas and Skenderis, Kostas and van
              Nieuwenhuizen, Peter},
     TITLE = {Loop calculations in quantum-mechanical non-linear sigma
              models},
   JOURNAL = {Nuclear Phys.~B},
  FJOURNAL = {Nuclear Physics. B. Theoretical, Phenomenological, and
              Experimental High Energy Physics. Quantum Field Theory and
              Statistical Systems},
    VOLUME = {446},
      YEAR = {1995},
    NUMBER = {1-2},
     PAGES = {211--222},
       DOI = {10.1016/0550-3213(95)00241-J},
       URL = {https://doi.org/10.1016/0550-3213(95)00241-J},
    EPRINT = {hep-th/9504097},
}

@article {bacova1,
    AUTHOR = {Bastianelli, F. and Corradini, O. and van Nieuwenhuizen, P.},
     TITLE = {Dimensional regularization of the path integral in curved
              space on an infinite time interval},
   JOURNAL = {Phys. Lett.~B},
  FJOURNAL = {Physics Letters. B. Particle Physics, Nuclear Physics and
              Cosmology},
    VOLUME = {490},
      YEAR = {2000},
    NUMBER = {1-2},
     PAGES = {154--162},
       DOI = {10.1016/S0370-2693(00)00978-3},
       URL = {https://doi.org/10.1016/S0370-2693(00)00978-3},
    EPRINT = {hep-th/0007105},
}

@article {bacova2,
    AUTHOR = {Bastianelli, F. and Corradini, O. and van Nieuwenhuizen, P.},
     TITLE = {Dimensional regularization of nonlinear sigma models on a
              finite time interval},
   JOURNAL = {Phys. Lett.~B},
  FJOURNAL = {Physics Letters. B. Particle Physics, Nuclear Physics and
              Cosmology},
    VOLUME = {494},
      YEAR = {2000},
    NUMBER = {1-2},
     PAGES = {161--167},
       DOI = {10.1016/S0370-2693(00)01180-1},
       URL = {https://doi.org/10.1016/S0370-2693(00)01180-1},
    EPRINT = {hep-th/0008045},
}

@book {basvan-book,
    AUTHOR = {Bastianelli, Fiorenzo and van Nieuwenhuizen, Peter},
     TITLE = {Path integrals and anomalies in curved space},
    SERIES = {Cambridge Monographs on Mathematical Physics},
 PUBLISHER = {Cambridge University Press, Cambridge},
      YEAR = {2006},
     PAGES = {xviii+379},
       DOI = {10.1017/CBO9780511535031},
       URL = {https://doi.org/10.1017/CBO9780511535031},
}

@article {Bastianelli:2002fv,
    AUTHOR = {Bastianelli, Fiorenzo and Zirotti, Andrea},
     TITLE = {Worldline formalism in a gravitational background},
   JOURNAL = {Nuclear Phys.~B},
  FJOURNAL = {Nuclear Physics. B. Theoretical, Phenomenological, and
              Experimental High Energy Physics. Quantum Field Theory and
              Statistical Systems},
    VOLUME = {642},
      YEAR = {2002},
    NUMBER = {1-2},
     PAGES = {372--388},
       DOI = {10.1016/S0550-3213(02)00683-1},
       URL = {https://doi.org/10.1016/S0550-3213(02)00683-1},
    EPRINT = {hep-th/0205182},
}

@article {Bastianelli:2012bz,
    AUTHOR = {Bastianelli, F. and Corradini, O. and D\'avila, J. M. and Schubert, C.},
     TITLE = {On the low-energy limit of one-loop photon-graviton amplitudes},
   JOURNAL = {Phys. Lett.~B},
  FJOURNAL = {Physics Letters. B. Particle Physics, Nuclear Physics and
              Cosmology},
    VOLUME = {716},
      YEAR = {2012},
    NUMBER = {2},
     PAGES = {345--349},
       DOI = {10.1016/j.physletb.2012.08.030},
       URL = {https://doi.org/10.1016/j.physletb.2012.08.030},
    EPRINT = {1202.4502},
}

@article {Bastianelli:2013tsa,
    AUTHOR = {Bastianelli, Fiorenzo and Bonezzi, Roberto},
     TITLE = {One-loop quantum gravity from a worldline viewpoint},
   JOURNAL = {J.~High Energy Phys.},
  FJOURNAL = {Journal of High Energy Physics},
    VOLUME = {2013},
      YEAR = {2013},
    NUMBER = {7},
     PAGES = {no.~7, 016, 23~pages},
       DOI = {10.1007/JHEP07(2013)016},
       URL = {https://doi.org/10.1007/JHEP07(2013)016},
    EPRINT = {1304.7135},
}

@article {Bastianelli:2019xhi,
    AUTHOR = {Bastianelli, Fiorenzo and Bonezzi, Roberto and Corradini,
              Olindo and Latini, Emanuele},
     TITLE = {One-loop quantum gravity from the {$\mathcal N = 4$} spinning
              particle},
   JOURNAL = {J.~High Energy Phys.},
  FJOURNAL = {Journal of High Energy Physics},
    VOLUME = {2019},
      YEAR = {2019},
    NUMBER = {11},
     PAGES = {no.~11, 124, 15~pages},
       DOI = {10.1007/jhep11(2019)124},
       URL = {https://doi.org/10.1007/jhep11(2019)124},
    EPRINT = {1909.05750},
}

@article {125,
    AUTHOR = {Ahmadiniaz, Naser and Balli, Filippo Maria and Corradini,
              Olindo and D\'avila, Jos\'e Manuel and Schubert, Christian},
     TITLE = {Compton-like scattering of a scalar particle with {$N$}
              photons and one graviton},
   JOURNAL = {Nuclear Phys.~B},
  FJOURNAL = {Nuclear Physics. B. Theoretical, Phenomenological, and
              Experimental High Energy Physics. Quantum Field Theory and
              Statistical Systems},
    VOLUME = {950},
      YEAR = {2020},
     PAGES = {114877, 21~pages},
       DOI = {10.1016/j.nuclphysb.2019.114877},
       URL = {https://doi.org/10.1016/j.nuclphysb.2019.114877},
    EPRINT = {1908.03425},
}

@article {Bastianelli:2008cu,
    AUTHOR = {Bastianelli, Fiorenzo and D\'avila, Jos\'e Manuel and Schubert, Christian},
     TITLE = {Gravitational corrections to the {E}uler--{H}eisenberg {L}agrangian},
   JOURNAL = {J.~High Energy Phys.},
  FJOURNAL = {Journal of High Energy Physics},
    VOLUME = {2009},
      YEAR = {2009},
    NUMBER = {3},
     PAGES = {no.~3, 086, 26~pages},
       DOI = {10.1088/1126-6708/2009/03/086},
       URL = {https://doi.org/10.1088/1126-6708/2009/03/086},
    EPRINT = {0812.4849},
}

@article {Hollowood:2007ku,
    AUTHOR = {Hollowood, Timothy J. and Shore, Graham M.},
     TITLE = {The refractive index of curved spacetime: the fate of
              causality in {QED}},
   JOURNAL = {Nuclear Phys.~B},
  FJOURNAL = {Nuclear Physics. B. Theoretical, Phenomenological, and
              Experimental High Energy Physics. Quantum Field Theory and
              Statistical Systems},
    VOLUME = {795},
      YEAR = {2008},
    NUMBER = {1-2},
     PAGES = {138--171},
       DOI = {10.1016/j.nuclphysb.2007.11.034},
       URL = {https://doi.org/10.1016/j.nuclphysb.2007.11.034},
    EPRINT = {0707.2303},
}

@article {Bastianelli:2004zp,
    AUTHOR = {Bastianelli, Fiorenzo and Schubert, Christian},
     TITLE = {One loop photon-graviton mixing in an electromagnetic field: part~1},
   JOURNAL = {J.~High Energy Phys.},
  FJOURNAL = {Journal of High Energy Physics. A SISSA Journal},
    VOLUME = {2005},
      YEAR = {2005},
    NUMBER = {2},
     PAGES = {no.~2, 069, 21~pages},
       DOI = {10.1088/1126-6708/2005/02/069},
       URL = {https://doi.org/10.1088/1126-6708/2005/02/069},
    EPRINT = {gr-qc/0412095},
}

@article {Bastianelli:2007jv,
    AUTHOR = {Bastianelli, F. and Nucamendi, U. and Schubert, C. and
              Villanueva, V. M.},
     TITLE = {One loop photon-graviton mixing in an electromagnetic field: part~2},
   JOURNAL = {J.~High Energy Phys.},
  FJOURNAL = {Journal of High Energy Physics. A SISSA Journal},
    VOLUME = {2007},
      YEAR = {2007},
    NUMBER = {11},
     PAGES = {no.~11, 099, 23~pages},
       DOI = {10.1088/1126-6708/2007/11/099},
       URL = {https://doi.org/10.1088/1126-6708/2007/11/099},
    EPRINT = {0710.5572},
}

@article {cecgir,
    AUTHOR = {Cecotti, S. and Girardello, L.},
     TITLE = {Functional measure, topology and dynamical supersymmetry
              breaking},
   JOURNAL = {Phys. Lett.~B},
  FJOURNAL = {Physics Letters. B. Particle Physics, Nuclear Physics and
              Cosmology},
    VOLUME = {110},
      YEAR = {1982},
    NUMBER = {1},
     PAGES = {39--43},
       DOI = {10.1016/0370-2693(82)90947-9},
       URL = {https://doi.org/10.1016/0370-2693(82)90947-9},
}

@article {alvarezgaume,
    AUTHOR = {Alvarez-Gaum\'e, Luis},
     TITLE = {Supersymmetry and the {A}tiyah--{S}inger index theorem},
   JOURNAL = {Comm. Math. Phys.},
  FJOURNAL = {Communications in Mathematical Physics},
    VOLUME = {90},
      YEAR = {1983},
    NUMBER = {2},
     PAGES = {161--173},
       DOI = {10.1007/BF01205500},
       URL = {https://doi.org/10.1007/BF01205500},
}

@article {alvwit,
    AUTHOR = {Alvarez-Gaum\'e, Luis and Witten, Edward},
     TITLE = {Gravitational anomalies},
   JOURNAL = {Nuclear Phys.~B},
  FJOURNAL = {Nuclear Physics. B. Theoretical, Phenomenological, and
              Experimental High Energy Physics. Quantum Field Theory and
              Statistical Systems},
    VOLUME = {234},
      YEAR = {1984},
    NUMBER = {2},
     PAGES = {269--330},
       DOI = {10.1016/0550-3213(84)90066-X},
       URL = {https://doi.org/10.1016/0550-3213(84)90066-X},
}

@article {friwin,
    AUTHOR = {Friedan, D. and Windey, P.},
     TITLE = {Supersymmetric derivation of the {A}tiyah--{S}inger index and
              the chiral anomaly},
   JOURNAL = {Nuclear Phys.~B},
  FJOURNAL = {Nuclear Physics. B. Theoretical, Phenomenological, and
              Experimental High Energy Physics. Quantum Field Theory and
              Statistical Systems},
    VOLUME = {235},
      YEAR = {1984},
    NUMBER = {3},
     PAGES = {395--416},
       DOI = {10.1016/0550-3213(84)90506-6},
       URL = {https://doi.org/10.1016/0550-3213(84)90506-6},
}

@article {Bastianelli:2007pv,
    AUTHOR = {Bastianelli, Fiorenzo and Corradini, Olindo and Latini,
              Emanuele},
     TITLE = {Higher spin fields from a worldline perspective},
   JOURNAL = {J.~High Energy Phys.},
  FJOURNAL = {Journal of High Energy Physics. A SISSA Journal},
    VOLUME = {2007},
      YEAR = {2007},
    NUMBER = {2},
     PAGES = {no.~2, 072, 19~pages},
       DOI = {10.1088/1126-6708/2007/02/072},
       URL = {https://doi.org/10.1088/1126-6708/2007/02/072},
    EPRINT = {hep-th/0701055},
}

@article {Bastianelli:2012bn,
    AUTHOR = {Bastianelli, Fiorenzo and Bonezzi, Roberto and Corradini,
              Olindo and Latini, Emanuele},
     TITLE = {Effective action for higher spin fields on ({A})d{S}
              backgrounds},
   JOURNAL = {J.~High Energy Phys.},
  FJOURNAL = {Journal of High Energy Physics},
    VOLUME = {2012},
      YEAR = {2012},
    NUMBER = {12},
     PAGES = {no.~12, 113, 26~pages},
       DOI = {10.1007/JHEP12(2012)113},
       URL = {https://doi.org/10.1007/JHEP12(2012)113},
    EPRINT = {1210.4649},
}

@article {Bonezzi:2012vr,
    AUTHOR = {Bonezzi, R. and Corradini, O. and Franchino Vi\~{n}as, S. A. and
              Pisani, P. A. G.},
     TITLE = {Worldline approach to noncommutative field theory},
   JOURNAL = {J.~Phys.~A: Math. Theor.},
  FJOURNAL = {Journal of Physics. A. Mathematical and Theoretical},
    VOLUME = {45},
      YEAR = {2012},
    NUMBER = {40},
     PAGES = {405401, 15~pages},
       DOI = {10.1088/1751-8113/45/40/405401},
       URL = {https://doi.org/10.1088/1751-8113/45/40/405401},
    EPRINT = {1204.1013},
}

@article {Kiem:2001dm,
    AUTHOR = {Kiem, Youngjai and Kim, Yeonjung and Ryou, Cheol and Sato,
              Haru-Tada},
     TITLE = {One-loop noncommutative {$\rm U(1)$} gauge theory from bosonic
              worldline approach},
   JOURNAL = {Nuclear Phys.~B},
  FJOURNAL = {Nuclear Physics. B. Theoretical, Phenomenological, and
              Experimental High Energy Physics. Quantum Field Theory and
              Statistical Systems},
    VOLUME = {630},
      YEAR = {2002},
    NUMBER = {1-2},
     PAGES = {55--86},
       DOI = {10.1016/S0550-3213(02)00182-7},
       URL = {https://doi.org/10.1016/S0550-3213(02)00182-7},
    EPRINT = {hep-th/0112176},
}

@article {NCU1,
    AUTHOR = {Ahmadiniaz, Naser and Corradini, Olindo and D'Ascanio, Daniela
              and Estrada-Jim\'enez, Sendic and Pisani, Pablo},
     TITLE = {Noncommutative {$\rm U(1)$} gauge theory from a worldline
              perspective},
   JOURNAL = {J.~High Energy Phys.},
  FJOURNAL = {Journal of High Energy Physics},
    VOLUME = {2015},
      YEAR = {2015},
    NUMBER = {11},
     PAGES = {no.~11, 069, 28~pages},
       DOI = {10.1007/JHEP11(2015)069},
       URL = {https://doi.org/10.1007/JHEP11(2015)069},
    EPRINT = {1507.07033},
}

@article {NCUN,
    AUTHOR = {Ahmadiniaz, Naser and Corradini, Olindo and Edwards, James P.
              and Pisani, Pablo},
     TITLE = {{${\rm U}(N)$} {Y}ang--{M}ills in non-commutative space time},
   JOURNAL = {J.~High Energy Phys.},
  FJOURNAL = {Journal of High Energy Physics},
    VOLUME = {2019},
      YEAR = {2019},
    NUMBER = {4},
     PAGES = {no.~4, 067, 34~pages},
       DOI = {10.1007/jhep04(2019)067},
       URL = {https://doi.org/10.1007/jhep04(2019)067},
    EPRINT = {1811.07362},
}

@article {Bastianelli:2006hq,
    AUTHOR = {Bastianelli, Fiorenzo and Corradini, Olindo and Pisani, Pablo
              A. G.},
     TITLE = {Worldline approach to quantum field theories on flat manifolds
              with boundaries},
   JOURNAL = {J.~High Energy Phys.},
  FJOURNAL = {Journal of High Energy Physics. A SISSA Journal},
    VOLUME = {2007},
      YEAR = {2007},
    NUMBER = {2},
     PAGES = {no.~2, 059, 18~pages},
       DOI = {10.1088/1126-6708/2007/02/059},
       URL = {https://doi.org/10.1088/1126-6708/2007/02/059},
    EPRINT = {hep-th/0612236},
}

@article {Bastianelli:2008vh,
    AUTHOR = {Bastianelli, Fiorenzo and Corradini, Olindo and Pisani, Pablo
              A. G. and Schubert, Christian},
     TITLE = {Scalar heat kernel with boundary in the worldline formalism},
   JOURNAL = {J.~High Energy Phys.},
  FJOURNAL = {Journal of High Energy Physics. A SISSA Journal},
    VOLUME = {2008},
      YEAR = {2008},
    NUMBER = {10},
     PAGES = {no.~10, 095, 21~pages},
       DOI = {10.1088/1126-6708/2008/10/095},
       URL = {https://doi.org/10.1088/1126-6708/2008/10/095},
    EPRINT = {0809.0652},
}

@article {ConfinedScalar,
    AUTHOR = {Corradini, Olindo and Edwards, James P. and Huet, Idrish and
              Manzo, Lucas and Pisani, Pablo},
     TITLE = {Worldline formalism for a confined scalar field},
   JOURNAL = {J.~High Energy Phys.},
  FJOURNAL = {Journal of High Energy Physics},
    VOLUME = {2019},
      YEAR = {2019},
    NUMBER = {8},
     PAGES = {no.~8, 037, 20~pages},
       DOI = {10.1007/jhep08(2019)037},
       URL = {https://doi.org/10.1007/jhep08(2019)037},
    EPRINT = {1905.00945},
}

@article {gielan,
    AUTHOR = {Gies, Holger and Langfeld, Kurt},
     TITLE = {Quantum diffusion of magnetic fields in a numerical worldline approach},
   JOURNAL = {Nuclear Phys.~B},
  FJOURNAL = {Nuclear Physics. B. Theoretical, Phenomenological, and
              Experimental High Energy Physics. Quantum Field Theory and
              Statistical Systems},
    VOLUME = {613},
      YEAR = {2001},
    NUMBER = {1-2},
     PAGES = {353--365},
       DOI = {10.1016/S0550-3213(01)00377-7},
       URL = {https://doi.org/10.1016/S0550-3213(01)00377-7},
    EPRINT = {hep-ph/0102185},
}

@article {124,
    AUTHOR = {Edwards, James P. and Gerber, Urs and Schubert, Christian and
              Trejo, Maria Anabel and Tsiftsi, Thomai and Weber, Axel},
     TITLE = {Applications of the worldline {M}onte {C}arlo formalism in
              quantum mechanics},
   JOURNAL = {Ann. Physics},
  FJOURNAL = {Annals of Physics},
    VOLUME = {411},
      YEAR = {2019},
     PAGES = {167966, 44~pages},
       DOI = {10.1016/j.aop.2019.167966},
       URL = {https://doi.org/10.1016/j.aop.2019.167966},
    EPRINT = {2019.16796},
}

@article {nietjoPRL,
    AUTHOR = {Nieuwenhuis, Taco and Tjon, J. A.},
     TITLE = {Nonperturbative study of generalized ladder graphs in a $\varphi^2 \chi$ theory},
   JOURNAL = {Phys. Rev. Lett.},
  FJOURNAL = {Physical Review Letters},
    VOLUME = {77},
      YEAR = {1996},
    NUMBER = {5},
     PAGES = {814--817},
       DOI = {10.1103/PhysRevLett.77.814},
       URL = {https://doi.org/10.1103/PhysRevLett.77.814},
    EPRINT = {hep-ph/9606403},
}

@article {gilamo,
    AUTHOR = {Gies, Holger and Langfeld, Kurt and Moyaerts, Laurent},
     TITLE = {Casimir effect on the worldline},
   JOURNAL = {J.~High Energy Phys.},
  FJOURNAL = {Journal of High Energy Physics. A SISSA Journal},
    VOLUME = {2003},
      YEAR = {2003},
    NUMBER = {6},
     PAGES = {no.~6, 018, 29~pages},
       DOI = {10.1088/1126-6708/2003/06/018},
       URL = {https://doi.org/10.1088/1126-6708/2003/06/018},
    EPRINT = {hep-th/0303264},
}

@article {giekli,
    AUTHOR = {Gies, Holger and Klingm\"uller, Klaus},
     TITLE = {Pair production in inhomogeneous fields},
   JOURNAL = {Phys. Rev.~D},
  FJOURNAL = {Physical Review D},
    VOLUME = {72},
      YEAR = {2005},
    NUMBER = {6},
     PAGES = {065001, 11~pages},
       DOI = {10.1103/PhysRevD.72.065001},
       URL = {https://doi.org/10.1103/PhysRevD.72.065001},
    EPRINT = {hep-ph/0505099},
}

@article {cormur,
    AUTHOR = {Corradini, Olindo and Muratori, Maurizio},
     TITLE = {A {M}onte {C}arlo approach to the worldline formalism in
              curved space},
   JOURNAL = {J.~High Energy Phys.},
  FJOURNAL = {Journal of High Energy Physics},
    VOLUME = {2020},
      YEAR = {2020},
    NUMBER = {11},
     PAGES = {no.~11, 169, 22~pages},
       DOI = {10.1007/jhep11(2020)169},
       URL = {https://doi.org/10.1007/jhep11(2020)169},
    EPRINT = {2006.02911},
}

@article {afalma,
    AUTHOR = {Affleck, I. K. and Alvarez, O. and Manton, N. S.},
     TITLE = {Pair production at strong coupling in weak external fields},
   JOURNAL = {Nuclear Phys.~B},
  FJOURNAL = {Nuclear Physics. B. Theoretical, Phenomenological, and
              Experimental High Energy Physics. Quantum Field Theory and
              Statistical Systems},
    VOLUME = {197},
      YEAR = {1982},
    NUMBER = {3},
     PAGES = {509--519},
       DOI = {10.1016/0550-3213(82)90455-2},
       URL = {https://doi.org/10.1016/0550-3213(82)90455-2},
}

@article {63,
    AUTHOR = {Dunne, Gerald V. and Schubert, Christian},
     TITLE = {Worldline instantons and pair production in inhomogenous
              fields},
   JOURNAL = {Phys. Rev.~D},
  FJOURNAL = {Physical Review. D. Third Series},
    VOLUME = {72},
      YEAR = {2005},
    NUMBER = {10},
     PAGES = {105004, 12~pages},
       DOI = {10.1103/PhysRevD.72.105004},
       URL = {https://doi.org/10.1103/PhysRevD.72.105004},
    EPRINT = {hep-th/0507174},
}

@article {bacozi1,
    AUTHOR = {Bastianelli, Fiorenzo and Corradini, Olindo and Zirotti,
              Andrea},
     TITLE = {B{RST} treatment of zero modes for the worldline formalism in
              curved space},
   JOURNAL = {J.~High Energy Phys.},
  FJOURNAL = {Journal of High Energy Physics. A SISSA Journal},
    VOLUME = {2004},
      YEAR = {2004},
    NUMBER = {1},
     PAGES = {no.~1, 023, 34~pages},
       DOI = {10.1088/1126-6708/2004/01/023},
       URL = {https://doi.org/10.1088/1126-6708/2004/01/023},
    EPRINT = {hep-th/0312064},
}

@article {fradkin66,
    AUTHOR = {Fradkin, E. S.},
     TITLE = {Application of functional methods in quantum field theory and quantum statistics.~{II}},
   JOURNAL = {Nuclear Phys.},
  FJOURNAL = {Nuclear Physics},
    VOLUME = {76},
      YEAR = {1966},
     PAGES = {588--624},
       DOI = {10.1016/0029-5582(66)90200-8},
       URL = {https://doi.org/10.1016/0029-5582(66)90200-8},
}

@article {Balachandran:1976ya,
    AUTHOR = {Balachandran, A. P. and Salomonson, Per and Skagerstam, Bo-Sture and Winnberg, Jan-Olov},
     TITLE = {Classical description of a particle interacting with a non-Abelian gauge field},
   JOURNAL = {Phys. Rev.~D},
  FJOURNAL = {Physical Review D},
    VOLUME = {15},
      YEAR = {1977},
    NUMBER = {8},
     PAGES = {2308--2317},
       DOI = {10.1103/PhysRevD.15.2308},
       URL = {https://doi.org/10.1103/PhysRevD.15.2308},
}

@article {Barducci:1976xq,
    AUTHOR = {Barducci, A. and Casalbuoni, R. and Lusanna, L.},
     TITLE = {Classical scalar and spinning particles interacting with external {Y}ang--{M}ills fields},
   JOURNAL = {Nuclear Phys.~B},
  FJOURNAL = {Nuclear Physics. B. Theoretical, Phenomenological, and
              Experimental High Energy Physics. Quantum Field Theory and
              Statistical Systems},
    VOLUME = {124},
      YEAR = {1977},
    NUMBER = {1},
     PAGES = {93--108},
       DOI = {10.1016/0550-3213(77)90278-4},
       URL = {https://doi.org/10.1016/0550-3213(77)90278-4},
}

@article {Bastianelli:2013pta,
    AUTHOR = {Bastianelli, Fiorenzo and Bonezzi, Roberto and Corradini,
              Olindo and Latini, Emanuele},
     TITLE = {Particles with non abelian charges},
   JOURNAL = {J.~High Energy Phys.},
  FJOURNAL = {Journal of High Energy Physics},
    VOLUME = {2013},
      YEAR = {2013},
    NUMBER = {10},
     PAGES = {no.~10, 098, 13~pages},
       DOI = {10.1007/JHEP10(2013)098},
       URL = {https://doi.org/10.1007/JHEP10(2013)098},
    EPRINT = {1309.1608},
}

@article {Ahmadiniaz:2015xoa,
    AUTHOR = {Ahmadiniaz, Naser and Bastianelli, Fiorenzo and Corradini,
              Olindo},
     TITLE = {Dressed scalar propagator in a non-{A}belian background from
              the worldline formalism},
   JOURNAL = {Phys. Rev.~D},
  FJOURNAL = {Physical Review D},
    VOLUME = {93},
      YEAR = {2016},
    NUMBER = {2},
     PAGES = {0250335, 13~pages},
       DOI = {10.1103/PhysRevD.93.025035},
       URL = {https://doi.org/10.1103/PhysRevD.93.025035},
      NOTE = {{A}ddendum, \href{https://doi.org/10.1103/PhysRevD.93.049904}{\textit{Phys. Rev.~D}} \textbf{93} (2016), 049904},
    EPRINT = {1508.05144},
}

@mics {136,
    AUTHOR = {Ahmadiniaz, Naser and Lopez-Arcos, Cristhiam  and Lopez-Lopez, Misha A. and Schubert, Christian},
     TITLE = {The {QED} four-photon amplitudes off-shell: part~1},
    EPRINT = {2012.11791},
}

@article {cotopi,
    AUTHOR = {Costantini, V. and De Tollis, B. and Pistoni, G.},
     TITLE = {Nonlinear effects in quantum electrodynamics},
   JOURNAL = {Nuovo Cimento~A},
  FJOURNAL = {Il Nuovo Cimento A},
    VOLUME = {2},
      YEAR = {1971},
    NUMBER = {3},
     PAGES = {733--787},
       DOI = {10.1007/BF02736745},
       URL = {https://doi.org/10.1007/BF02736745},
}

@mics {4photon,
    AUTHOR = {Ahmadiniaz, Naser and Lopez-Arcos, Cristhiam  and Lopez-Lopez, Misha A. and Schubert, Christian},
     TITLE = {The QED four-photon amplitudes off-shell: parts 2--4},
      NOTE = {{i}n preparation},
}

@article {brdekr,
    AUTHOR = {Broadhurst, D. J. and Delbourgo, R. and Kreimer, D.},
     TITLE = {Unknotting the polarized vacuum of quenched {QED}},
   JOURNAL = {Phys. Lett.~B},
  FJOURNAL = {Physics Letters. B. Particle Physics, Nuclear Physics and
              Cosmology},
    VOLUME = {421},
      YEAR = {19896},
    NUMBER = {1-4},
     PAGES = {421--428},
       DOI = {10.1016/0370-2693(95)01343-1},
       URL = {https://doi.org/10.1016/0370-2693(95)01343-1},
    EPRINT = {hep-ph/9509296},
}

@article {bckr,
    AUTHOR = {Baikov, P. A. and Chetyrkin, K. G. and K\"uhn, J. H. and Rittinger, J.},
     TITLE = {Vector correlator in massless {QCD} at order {$\mathcal{O}\big(\alpha_s^4\big)$} and the {QED} $\beta$-function at five loop},
   JOURNAL = {J.~High Energy Phys.},
  FJOURNAL = {Journal of High Energy Physics. A SISSA Journal},
    VOLUME = {2012},
      YEAR = {2012},
    NUMBER = {12},
     PAGES = {no.~12, 017, 14~pages},
       DOI = {10.1007/JHEP07(2012)017},
       URL = {https://doi.org/10.1007/JHEP07(2012)017},
    EPRINT = {1206.1284},
}

@article {56,
    AUTHOR = {Martin, Louise C. and Schubert, Christian and Villanueva Sandoval, Victor M.},
     TITLE = {On the low-energy limit of the {QED} {$N$}-photon amplitudes},
   JOURNAL = {Nuclear Phys.~B},
  FJOURNAL = {Nuclear Physics. B. Theoretical, Phenomenological, and
              Experimental High Energy Physics. Quantum Field Theory and
              Statistical Systems},
    VOLUME = {668},
      YEAR = {2003},
    NUMBER = {1-2},
     PAGES = {335--344},
       DOI = {10.1016/S0550-3213(03)00578-9},
       URL = {https://doi.org/10.1016/S0550-3213(03)00578-9},
    EPRINT = {hep-th/0301022},
}

@article {51,
    AUTHOR = {Dunne, Gerald V. and Schubert, Christian},
     TITLE = {Two-loop self-dual {E}uler--{H}eisenberg {L}agrangians. {I}.~{R}eal part and helicity amplitudes},
   JOURNAL = {J.~High Energy Phys.},
  FJOURNAL = {Journal of High Energy Physics. A SISSA Journal},
    VOLUME = {2002},
      YEAR = {2002},
    NUMBER = {8},
     PAGES = {no.~8, 053, 25~pages},
       DOI = {10.1088/1126-6708/2002/08/053},
       URL = {https://doi.org/10.1088/1126-6708/2002/08/053},
    EPRINT = {hep-th/0205004},
}

@article {giekar,
    AUTHOR = {Gies, Holger and Karbstein, Felix},
     TITLE = {An addendum to the {H}eisenberg--{E}uler effective action
              beyond one loop},
   JOURNAL = {J.~High Energy Phys.},
  FJOURNAL = {Journal of High Energy Physics},
    VOLUME = {2017},
      YEAR = {2017},
    NUMBER = {3},
     PAGES = {no.~3, 108, 35~pages},
       DOI = {10.1007/JHEP03(2017)108},
       URL = {https://doi.org/10.1007/JHEP03(2017)108},
    EPRINT = {1612.07251},
}

@article {118,
    AUTHOR = {Edwards, James P. and Huet, Adolfo and Schubert, Christian},
     TITLE = {On the low-energy limit of the {QED} {$N$}-photon amplitudes: part~2},
   JOURNAL = {Nuclear Phys.~B},
  FJOURNAL = {Nuclear Physics. B. Theoretical, Phenomenological, and
              Experimental High Energy Physics. Quantum Field Theory and
              Statistical Systems},
    VOLUME = {935},
      YEAR = {2018},
     PAGES = {198--209},
       DOI = {10.1016/j.nuclphysb.2018.07.026},
       URL = {https://doi.org/10.1016/j.nuclphysb.2018.07.026},
    EPRINT = {1807.10697},
}

@article {52,
    AUTHOR = {Dunne, Gerald V. and Schubert, Christian},
     TITLE = {Two-loop self-dual {E}uler--{H}eisenberg {L}agrangians. {II}.~{I}maginary part and {B}orel analysis},
   JOURNAL = {J.~High Energy Phys.},
  FJOURNAL = {Journal of High Energy Physics. A SISSA Journal},
    VOLUME = {2002},
      YEAR = {2002},
    NUMBER = {6},
     PAGES = {no.~6, 042, 29~pages},
       DOI = {10.1088/1126-6708/2002/06/042},
       URL = {https://doi.org/10.1088/1126-6708/2002/06/042},
    EPRINT = {hep-th/0205005},
}

@article {fapaza,
    AUTHOR = {Faber, C. and Pandharipande, R.},
     TITLE = {Hodge integrals and {G}romov--{W}itten theory},
   JOURNAL = {Invent. Math.},
  FJOURNAL = {Inventiones Mathematicae},
    VOLUME = {139},
      YEAR = {2000},
    NUMBER = {1},
     PAGES = {173--199},
       DOI = {10.1007/s002229900028},
       URL = {https://doi.org/10.1007/s002229900028},
    EPRINT = {math.AG/9810173},
}

@article {59,
    AUTHOR = {Dunne, Gerald V. and Schubert, Christian},
     TITLE = {Bernoulli number identities from quantum field theory and
              topological string theory},
   JOURNAL = {Commun. Number Theory Phys.},
  FJOURNAL = {Communications in Number Theory and Physics},
    VOLUME = {7},
      YEAR = {2013},
    NUMBER = {2},
     PAGES = {225--249},
       DOI = {10.4310/CNTP.2013.v7.n2.a1},
       URL = {https://doi.org/10.4310/CNTP.2013.v7.n2.a1},
    EPRINT = {math.NT/0406610},
}

@article {34,
    AUTHOR = {M\"uller, Uwe and Schubert, Christian},
     TITLE = {A quantum field theoretical representation of {E}uler--{Z}agier
              sums},
   JOURNAL = {Int.~J. Math. Math. Sci.},
  FJOURNAL = {International Journal of Mathematics and Mathematical
              Sciences},
    VOLUME = {31},
      YEAR = {2002},
    NUMBER = {3},
     PAGES = {127--148},
       DOI = {10.1155/S0161171202106028},
       URL = {https://doi.org/10.1155/S0161171202106028},
    EPRINT = {math.QA/9908067},
}

@book {polbook,
    AUTHOR = {Polyakov, A. M.},
     TITLE = {Gauge fields and strings},
    SERIES = {Contemporary Concepts in Physics},
    VOLUME = {3},
 PUBLISHER = {Harwood Academic Publishers, Chur},
      YEAR = {1987},
     PAGES = {x+301},
}

@article {fljeta,
    AUTHOR = {Fleischer, J. and Jegerlehner, F. and Tarasov, O. V.},
     TITLE = {A new hypergeometric representation of one-loop scalar
              integrals in {$d$} dimensions},
   JOURNAL = {Nuclear Phys.~B},
  FJOURNAL = {Nuclear Physics. B. Theoretical, Phenomenological, and
              Experimental High Energy Physics. Quantum Field Theory and
              Statistical Systems},
    VOLUME = {672},
      YEAR = {2003},
    NUMBER = {1-2},
     PAGES = {303--328},
       DOI = {10.1016/j.nuclphysb.2003.09.004},
       URL = {https://doi.org/10.1016/j.nuclphysb.2003.09.004},
    EPRINT = {hep-ph/0307113},
}

@article {davydychev,
    AUTHOR = {Davydychev, Andrei I.},
     TITLE = {Four-point function in general kinematics through geometrical splitting and reduction},
   JOURNAL = {J.~Phys. Conf. Ser.},
  FJOURNAL = {Journal of Physics: Conference Series},
    VOLUME = {1085},
      YEAR = {2018},
    NUMBER = {5},
     PAGES = {052016, 8~pages},
       DOI = {10.1088/1742-6596/1085/5/052016},
       URL = {https://doi.org/10.1088/1742-6596/1085/5/052016},
    EPRINT = {1711.07351},
}

@article {pharie,
    AUTHOR = {Phan, Khiem Hong and Riemann, Tord},
     TITLE = {Scalar 1-loop {F}eynman integrals as meromorphic functions in
              space-time dimension~{$d$}},
   JOURNAL = {Phys. Lett.~B},
  FJOURNAL = {Physics Letters. B. Particle Physics, Nuclear Physics and
              Cosmology},
    VOLUME = {791},
      YEAR = {2019},
     PAGES = {257--264},
       DOI = {10.1016/j.physletb.2019.02.044},
       URL = {https://doi.org/10.1016/j.physletb.2019.02.044},
    EPRINT = {1812.10975},
}

@article {6,
    AUTHOR = {Fliegner, Denny and Schmidt, Michael G. and Schubert, Christian},
     TITLE = {The higher derivative expansion of the effective action by the string-inspired method.~{I}},
   JOURNAL = {Z.~Phys.~C},
  FJOURNAL = {Zeitschrift f\"ur Physik C Particles and Fields},
    VOLUME = {64},
      YEAR = {1994},
     PAGES = {111--116},
       DOI = {10.1007/BF01557242},
       URL = {https://doi.org/10.1007/BF01557242},
    EPRINT = {hep-ph/9401221},
}
