Spectral analysis of the chiral quark soliton model

Abstract:
We present mathematically rigorous analysis of a Dirac operator $H$ describing the Hamiltonian of the chiral quark soliton model in nuclear physics. The following aspects are investigated:
    (i) a supersymmetric structure of the model;
    (ii) the identification of the essential spectrum of $H$;
    (iii) an upper bound for the number of discrete eignevalues of  $H$;
    (iv) existence of  discrete positive or negative ground states of $H$;
    (v) symmetry reduction of $H$.