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Borne T., Lochak G., Stumpf H. — Nonperturbative quantum field theory and the structure of matter
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Название: Nonperturbative quantum field theory and the structure of matterАвторы: Borne T., Lochak G., Stumpf H.Аннотация: In this book a new method of nonperturbative quantum field theory is developed which offers an alternative version of the common treatment of these problems, and which, in addition, is adapted to the investigation of composite particle dynamics and reactions, or, synonymously, to the investigation of the structure of matter. This new method is based on the Algebraic Schrodinger Representation of canonically quantized (relativistic) fields, and the derivation, formulation and application of this representation will be extensively discussed in Chapters 3, 4 and 5. In this method use is made of the Hamiltonian formalism in combination with elements of the algebraic representation theory of quantum fields and Heisenberg's equation of motion.
Язык: Рубрика: Физика /Физика твёрдого тела /Методы квантовой теории поля /Статус предметного указателя: Готов указатель с номерами страниц ed2k: ed2k stats Год издания: 2002Количество страниц: 332Добавлена в каталог: 27.07.2005Операции: Положить на полку |
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72 88 Afiine connection 278 Algebraic, Quantum Theory 70 Algebraic, Schroedinger Representation 97ff Angular momentum density 57 Anholonomic coordinates 277f Antisymmetric product 107 Auxiliary fields 54 184f Bargmann — Wigner equations 38 see Basis states, dual 103 Basis states, nonorthogonal 102ff 106ff Bethe — Salpeter equations 148 190 Bianchi identities 278f 292 Bosons, effective masses 211 244ff Bosons, electro-weak gauge 215 Bosons, observable substructures 250ff Bosons, W, Z 228ff 244 Bound state equations 150ff 174 Bound states 126ff 148ff Bound states, four-fermion 173ff Bound states, quantum numbers 160ff Bound states, scalar boson 156ff 245ff Bound states, three-particle 167ff 215ff Bound states, vector boson 155ff 159 244ff BRS-formalism 193 CAR algebra 58 73 113 Casimir operators 66 CCR algebra 132 Chain rule method 137ff 145 202 283 Charge 170f Chiral symmetry 41 46 Christoffel symbol 278 Clebsch — Gordon theorem 30 Composite particles 126ff Connection affme 278 Constraints phenomenological 199f 233ff Contraction technique 150ff Cosmological constant 35 Coupling, constant 293 Coupling, constant, effective 211 Coupling, of bosons and fermions 201ff Coupling, of fermions and gravitons 296ff Coupling, Yukawa 42 Covariant derivative 280 296 Covariant formalism 69 95f 120f 150ff Current density of fusion theory 15 26f Curvature 35 Curvature, scalar 278 Curvature, tensor 278ff Cyclic vector 106 113 de Broglie — Bargmann — Wigner equations 148ff 206 Decomposition theorem 52 Decoupling theorem 204 272 Dipole ghosts 41 Dirac equation in Riemann — Cartan space 280 Dirac vacuum 180 Direct forces 136ff Dressed particle, dynamics 144ff Dressed particle, states 127 140ff 293ff Dual functions 130 142 204ff 218 288 295f Effective, boson masses 211 244ff Effective, boson theory 132ff 208ff Effective, boson-fermion theory 144ff 201ff 219ff Effective, boson-fermion theory, with symmetry breaking 238ff Effective, coupling constant 211 Effective, electrodynamics 236ff Effective, fermion mass 225 Effective, graviton equations 289ff Effective, graviton-fermion theory 281 296ff Effective, quantization 259ff Effective, quantum Hamiltonians 259ff Effective, Yang — Mills equations 213f Einstein equations 278 Einstein theory 278ff Einstein theory, in anholonomic coordinates 280 Electric fields non-abelian 212ff Electro-weak gauge boson states 215 Electro-weak theory phenomenological 193ff 226ff Energy equation, for boson fields 135f 140ff Energy equation, for boson-fermion theory 146ff 203ff 222f Energy equation, for graviton-fermion theory 283 Energy equation, for non-abelian SU(N) theory 199f Energy equation, for subfermion fields, normal ordered version 92 94 Energy equation, for subfermion fields, time ordered version 86ff Energy equation, for subfermions single time version 117 119 Energy-momentum density 56 Energy-momentum density, of fusion theory 16 27f Equal time limit 120f Equivalence principle 280 Exchange forces 136ff Exchange forces, estimate of 271ff Expansion functions, for boson mapping 204f Expansion functions, for graviton mapping 285 Fermion mass effective 225 Feynman propator 150 Field operator 57 Fock, representation 69 Fock, vacuum 169 Functional equation, for boson fields 135f 140ff Functional equation, for boson-fermion theory 145f 203ff 222f Functional equation, for graviton-fermion theory 283 Functional equation, for non-abelian SU(N) theory 199f Functional equation, for spinor fields normal transformed 90 Functional equation, for subfermion fields, normal transformed 90 Functional equation, for subfermion fields, time ordered 84f Functional Quantum Theory 70f Functional, chain rule 139 202 283 Functional, generating 74 Functional, ground state 74 113 Functional, Hamiltonian operator 261ff Functional, Hamiltonian operator, for boson-fermion theory 146 203 Functional, Hamiltonian operator, for effective boson-fermion theory 222f Functional, Hamiltonian operator, for non-abelian gauge theory 200 238ff Functional, Hamiltonian operator, for subfermions 128 Functional, Heisenberg equation 212 Functional, space 71 73f Functional, space, bosonic 132 Functional, space, for coupling theories 202 Functional, space, single time version 113ff Functional, states 72ff 88 112 133 199f 202 282 Fusion, de Broglie's general method 24ff Fusion, principle 48 Fusion, theory 39ff Fusion, theory, de Broglie's 6ff Gauge fields, non-Abelian 193ff Gauge theory 102 193ff Gauge, fixing 235f Gauge, invariance 21 Gauge, Lorentz 12 Gauge, temporal 194f 197 205f 235f Gauss law 197f 214 233ff Geheniau formulae 16 Generators 62ff 76ff Glashow — Salam — Weinberg theory 194 226ff Glashow — Salam — Weinberg transformation 228 Gluon 249 276 GNS construction 70f 106ff Grand unification 47 Gravitation theory 276ff Gravitation theory, anholonomic 278ff Gravitation theory, in flat space 276f Graviton in fusion theory 29ff Graviton states 173ff 285ff Green's function 151f 253 294 Haag's theorem 69 Hamiltonian density, for local gauge theory 231 Hamiltonian density, for subfermions 56 101 Hamiltonian density, of composite photons 15 Hamiltonian formalism 97ff 120f Hamiltonian formalism, relativistic covariance 120ff Hard core, equation 129 Hard core, states 128ff Hausdorff formula 114 Heisenberg equation 101 112 115 Heisenberg equation, functional version 212 Heisenberg picture 67 Higgs mechanism 225 226ff Higher order equations 51ff Hypercharge 170f Indefinite metric 41 49 58 99ff Inequivalent representations 69 97 Klein — Gordon equation 12 Krein space 98 99ff Lagrangian, for subfermions 56 Lagrangian, of composite photons 15 Lagrangian, of local gauge theory 195 226f 230 Lehmann — Kaellen spectral theorem 131 Lepton states 167ff 214ff Lorentz group see “Poincare group” LSZ formalism 69 Magnetic fields non-abelian 212ff Mass of gravitons 35 Mass of photons 12 2 23 Matrix elements 72 Maxwell equations 12 183 Membranes 47 Metric indefinite 41 49 58 99ff Metric tensor 108f 143f 278 Metric tensor, for one-fermion states 181f Metric tensor, of Riemann space 34f Minimal coupling 280 monopole 14 Neutrino 21 NJL model 45 Norm conservation 179ff 184ff Normal ordering 87ff Normal ordering, functional 87ff Normal ordering, nonperturbative 87ff 118ff Normalization of states 109f 179f 254ff Operator product 42ff 126 190f Operator product, antisymmetric 107 Operator product, time ordered 72 82 95f Particle intepretation 169 Particles 40 Particles, spectrum of 244ff Path integrals 43ff 95 Pauli — Villars regularization 48 51 55f Phenomenological constraints 233ff Photon 4ff 42 190 Photon, electric 11 Photon, equations 7ff Photon, equations, effective 244 Photon, magnetic 14 Physical, potentials 21 Physical, states 188ff 244f 254ff Physical, subspace 100f Poincare gauge theories 299 Poincare group 48 61ff 76f Polarization cloud 127 221 282 Potentials physical 21 Probability, density for vector bosons 254 Probability, interpretation 184ff Proca equation 37 Propagator 88f 91 Propagator, Feynman 150 Propagator, free fermion 91ff Propagator, free fermion, single time version 118f 130f 207 Propagator, symmetry breaking 237 Quantization, effective 198 259ff Quantization, non-canonical 48f 58 Quantization, of non-abelian SU(N) theory 198f Quantization, of spinor fields 57f Quantum numbers, of three-particle states 169ff Quantum numbers, of two-particle states 160 Quark states 167ff 215ff Regularization 47ff 58 184ff 262f Regularization, nonperturbative 48 51 97 Regularization, Pauli — Villars 48 51 55f Relativistic covariance of Hamiltonian formalism 120ff Renormalization, vacuum 110 Renormalization, vertex 93f 120 Representation, Fock 69 Representation, GNS 70f 92 106ff Representation, inequivalent 69 97 Representation, of operators 104ff llOff Representation, of states contravariant 103 Representation, of states covariant 103 Residual interactions estimate of 265ff Ricci identities 278 291 Ricci tensor 278 Riemann space 278ff Riemann — Cartan geometry 288 292 Riemann — Christoffel tensor 34 278 Rishon model 50 Scalar boson states 156 160ff 246ff Scalar product 100 104 256 Scalar product, covariance of 123ff Scalar product, in functional space 76 114ff Scattering states 155 272 Schroedinger picture 67 Schwinger — Dyson — Freese equations 69 85 95 Secular equation for vector bosons 158 Shell model states 214ff Single time formalism see “Hamiltonian formalism” Spin, in fusion theory 29f Spin, of composite photons 18f 19ff Spinor field, equation 50 55 59f Spinor field, theory, Heisenberg's 40ff Spinor field, transformations 61f 67f Standard model 191 226 State space 69 97ff States, algebraic 70 States, bound 126ff 148ff States, electro-weak gauge boson 204 States, four-fermion 173ff States, functional 74 States, graviton 173ff 285ff States, lepton and quark 167ff 216ff States, normalization 109f States, physical 184ff 254ff States, scalar boson 156 160ff 246ff States, scattering 155 272 States, shell model 214ff States, three-particle 167ff 216ff States, vacuum 61 71 States, vector boson 155ff 204ff 251ff strings 47 Strong mapping 42ff 190f Subfermions 49f 125 Subfermions, angular momentum density 57 Subfermions, energy-momentum density 56 Subfermions, Hamiltonian density 56 Subfermions, Lagrangian density 55 Super-index 59 197 Superspinor 59 Supersymmetry 47 Symmetry breaking 226ff Symmetry breaking, by vacuum state 236ff Symmetry breaking, in effective gravitation 288 Symmetry chiral 46 Symmetry conditions 61ff Symmetry conditions, for 79 Symmetry conditions, for functional states 79 90 Symmetry conditions, of three-particle states 168ff Symmetry conditions, of vector boson states 160ff Tamm — Dancoff method 41 71 99 Temporal gauge 194f 197 205f 235f Tensor functions for graviton states 176ff Tetrads 279
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