%PDF-1.4 % 5 0 obj << /S /GoTo /D (section.1) >> endobj 8 0 obj (1 Introduction) endobj 9 0 obj << /S /GoTo /D (section.2) >> endobj 12 0 obj (2 Definition of the Nelson model and preliminaries) endobj 13 0 obj << /S /GoTo /D (subsection.2.1) >> endobj 16 0 obj (2.1 Fock-space) endobj 17 0 obj << /S /GoTo /D (subsection.2.2) >> endobj 20 0 obj (2.2 The Nelson model Hamiltonian H in the Fock representation) endobj 21 0 obj << /S /GoTo /D (subsection.2.3) >> endobj 24 0 obj (2.3 Operator and domain definitions) endobj 25 0 obj << /S /GoTo /D (subsection.2.4) >> endobj 28 0 obj (2.4 Self-adjointness of H) endobj 29 0 obj << /S /GoTo /D (subsection.2.5) >> endobj 32 0 obj (2.5 Translational invariance of H) endobj 33 0 obj << /S /GoTo /D (subsection.2.6) >> endobj 36 0 obj (2.6 Removing the ultraviolet cutoff in FN) endobj 37 0 obj << /S /GoTo /D (subsection.2.7) >> endobj 40 0 obj (2.7 Why is the existence of H"0362H not enough?) endobj 41 0 obj << /S /GoTo /D (subsection.2.8) >> endobj 44 0 obj (2.8 Fundamental questions) endobj 45 0 obj << /S /GoTo /D (section.3) >> endobj 48 0 obj (3 Classical field theory) endobj 49 0 obj << /S /GoTo /D (subsection.3.1) >> endobj 52 0 obj (3.1 Why fields?) endobj 53 0 obj << /S /GoTo /D (subsection.3.2) >> endobj 56 0 obj (3.2 The classical Klein-Gordon field) endobj 57 0 obj << /S /GoTo /D (subsubsection.3.2.1) >> endobj 60 0 obj (3.2.1 The free field) endobj 61 0 obj << /S /GoTo /D (subsubsection.3.2.2) >> endobj 64 0 obj (3.2.2 Scalar interaction) endobj 65 0 obj << /S /GoTo /D (subsubsection.3.2.3) >> endobj 68 0 obj (3.2.3 Green's function) endobj 69 0 obj << /S /GoTo /D (subsection.3.3) >> endobj 72 0 obj (3.3 The static classical Nelson model) endobj 73 0 obj << /S /GoTo /D (subsection.3.4) >> endobj 76 0 obj (3.4 The dynamic classical Nelson model) endobj 77 0 obj << /S /GoTo /D (section.4) >> endobj 80 0 obj (4 Quantum field theory) endobj 81 0 obj << /S /GoTo /D (subsection.4.1) >> endobj 84 0 obj (4.1 Motivation for a quantum version of the theory of fields) endobj 85 0 obj << /S /GoTo /D (subsection.4.2) >> endobj 88 0 obj (4.2 The quantum Klein-Gordon field) endobj 89 0 obj << /S /GoTo /D (subsubsection.4.2.1) >> endobj 92 0 obj (4.2.1 The free field) endobj 93 0 obj << /S /GoTo /D (subsubsection.4.2.2) >> endobj 96 0 obj (4.2.2 Scalar interaction) endobj 97 0 obj << /S /GoTo /D (subsubsection.4.2.3) >> endobj 100 0 obj (4.2.3 Comment on the choice of representation of the commutator algebra) endobj 101 0 obj << /S /GoTo /D (subsection.4.3) >> endobj 104 0 obj (4.3 Toy model) endobj 105 0 obj << /S /GoTo /D (subsubsection.4.3.1) >> endobj 108 0 obj (4.3.1 Definition of the model) endobj 109 0 obj << /S /GoTo /D (subsubsection.4.3.2) >> endobj 112 0 obj (4.3.2 Self-adjointness of T) endobj 113 0 obj << /S /GoTo /D (subsubsection.4.3.3) >> endobj 116 0 obj (4.3.3 Perturbation theory) endobj 117 0 obj << /S /GoTo /D (subsubsection.4.3.4) >> endobj 120 0 obj (4.3.4 The renormalized model Hamiltonian T"0362T) endobj 121 0 obj << /S /GoTo /D (subsubsection.4.3.5) >> endobj 124 0 obj (4.3.5 What does T"0362T look like?) endobj 125 0 obj << /S /GoTo /D (subsubsection.4.3.6) >> endobj 128 0 obj (4.3.6 What does D\(T"0362T\) look like?) endobj 129 0 obj << /S /GoTo /D (subsubsection.4.3.7) >> endobj 132 0 obj (4.3.7 What does the action of T"0362T on elements in D\(T"0362T\) look like?) endobj 133 0 obj << /S /GoTo /D (subsubsection.4.3.8) >> endobj 136 0 obj (4.3.8 A physical interpretation for this toy model) endobj 137 0 obj << /S /GoTo /D (subsection.4.4) >> endobj 140 0 obj (4.4 The static quantum Nelson model) endobj 141 0 obj << /S /GoTo /D (subsection.4.5) >> endobj 144 0 obj (4.5 The dynamic quantum Nelson model) endobj 145 0 obj << /S /GoTo /D (subsubsection.4.5.1) >> endobj 148 0 obj (4.5.1 Perturbation theory) endobj 149 0 obj << /S /GoTo /D (subsubsection.4.5.2) >> endobj 152 0 obj (4.5.2 The renormalized model Hamiltonian H"0362H and its ground state) endobj 153 0 obj << 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