%PDF-1.4 5 0 obj << /S /GoTo /D (section.1) >> endobj 8 0 obj (1 Introduction) endobj 9 0 obj << /S /GoTo /D (subsection.1.1) >> endobj 12 0 obj (1.1 Integration extension in finite dimensions) endobj 13 0 obj << /S /GoTo /D (subsection.1.2) >> endobj 16 0 obj (1.2 Overview on the extension of field theoretic Weyl quantization) endobj 17 0 obj << /S /GoTo /D (section.2) >> endobj 20 0 obj (2 Preliminary notions and results) endobj 21 0 obj << /S /GoTo /D (subsection.2.1) >> endobj 24 0 obj (2.1 The notion of strict deformation quantization) endobj 25 0 obj << /S /GoTo /D (subsection.2.2) >> endobj 28 0 obj (2.2 Weyl algebra) endobj 29 0 obj << /S /GoTo /D (subsection.2.3) >> endobj 32 0 obj (2.3 *-isomorphisms for the quantum Weyl algebras) endobj 33 0 obj << /S /GoTo /D (subsection.2.4) >> endobj 36 0 obj (2.4 Strict deformation quantization for C*-Weyl algebras) endobj 37 0 obj << /S /GoTo /D (subsection.2.5) >> endobj 40 0 obj (2.5 Geometry and algebraization of a classical field theory) endobj 41 0 obj << /S /GoTo /D (section.3) >> endobj 44 0 obj (3 Strict deformation quantization via Banach-*-algebras of measures) endobj 45 0 obj << /S /GoTo /D (subsection.3.1) >> endobj 48 0 obj (3.1 Inductive limit of regular Borel measures) endobj 49 0 obj << /S /GoTo /D (subsection.3.2) >> endobj 52 0 obj (3.2 Non-commutative Banach-*-algebras of measures) endobj 53 0 obj << /S /GoTo /D (subsection.3.3) >> endobj 56 0 obj (3.3 Poisson algebras of measures) endobj 57 0 obj << /S /GoTo /D (subsection.3.4) >> endobj 60 0 obj (3.4 Strict deformation quantization of Banach-*-type) endobj 61 0 obj << /S /GoTo /D (section.4) >> endobj 64 0 obj (4 Poisson algebras of phase space functions) endobj 65 0 obj << /S /GoTo /D (subsection.4.1) >> endobj 68 0 obj (4.1 Fourier transformation of the measure algebras) endobj 69 0 obj << /S /GoTo /D (subsection.4.2) >> endobj 72 0 obj (4.2 Pre-symplectic geometry revisited) endobj 73 0 obj << /S /GoTo /D (section.5) >> endobj 76 0 obj (5 Representations, folia, and enveloping C*-algebras) endobj 77 0 obj << /S /GoTo /D (subsection.5.1) >> endobj 80 0 obj (5.1 Folia and quasi-equivalence classes of representations) endobj 81 0 obj << /S /GoTo /D (subsection.5.2) >> endobj 84 0 obj (5.2 -continuous representations of the Weyl algebra) endobj 85 0 obj << /S /GoTo /D (subsection.5.3) >> endobj 88 0 obj (5.3 Folium of regular states of the Weyl algebra) endobj 89 0 obj << /S /GoTo /D (subsection.5.4) >> endobj 92 0 obj (5.4 Representations of the measure Banach-*-algebras) endobj 93 0 obj << /S /GoTo /D (section.6) >> endobj 96 0 obj (6 Extended Weyl quantization as strict deformation quantization \(of C*-type\)) endobj 97 0 obj << /S /GoTo /D (subsection.6.1) >> endobj 100 0 obj (6.1 Families of representations, quantization maps) endobj 101 0 obj << /S /GoTo /D (subsection.6.2) >> endobj 104 0 obj (6.2 Dirac's and von Neumann's conditions) endobj 105 0 obj << /S /GoTo /D (subsection.6.3) >> endobj 108 0 obj (6.3 On Rieffel's continuity condition) endobj 109 0 obj << /S /GoTo /D (subsubsection.6.3.1) >> endobj 112 0 obj (6.3.1 Non-degenerate symplectic form ) endobj 113 0 obj << /S /GoTo /D (subsubsection.6.3.2) >> endobj 116 0 obj (6.3.2 Degenerate , well-matched representation families) endobj 117 0 obj << /S /GoTo /D (section.A) >> endobj 120 0 obj (A E'-invariant folia and representations) endobj 121 0 obj << /S /GoTo /D (section.B) >> endobj 124 0 obj (B Proofs of the Propositions 5 and 4) endobj 125 0 obj << /S /GoTo /D (ref.1) >> endobj 128 0 obj (References) endobj 129 0 obj << /S /GoTo /D [130 0 R /Fit ] >> endobj 132 0 obj << /Length 4308 /Filter /FlateDecode >> stream xڽZYF~_G z/Ab'ab