http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
introduction to non-perturbative foundations of quantum field theory
This volume discusses fundamental aspects of quantum field theory and of gauge theories, with attention to mathematical consistency. Basic issues of the standard model of elementary particles (Higgs mechanism and chiral symmetry breaking in quantum chromodynamics) are treated without relying on the perturbative expansion and on instanton calculus.
Cover; Contents; 1 Relativistic quantum mechanics; 1 Quantum mechanics and relativity; 2 Relativistic Schrödinger wave mechanics; 2.1 Relativistic Schrödinger equation; 2.2 Klein-Gordon equation; 2.3 Dirac equation; 2.4 The general conflict between locality and energy positivity; 3 Relativistic particle interactions and quantum mechanics; 3.1 Problems of relativistic particle interactions; 3.2 Field interactions and quantum mechanics; 4 Free field equations and quantum mechanics; 5 Particles as field quanta; 6 Appendix: The Dirac equation; 7 Appendix: Canonical field theory
2 Mathematical problems of the perturbative expansion1 Dyson's perturbative expansion; 2 Dyson argument against convergence; 2.1(Omitted) [Sup(4)] model in zero dimensions; 2.2 (Omitted)[Sup(4)] model in 0+1 dimensions; 2.3 (Omitted)[Sup(4)] 4 model in 1+1 and 2+1 dimensions; 3 Haag theorem; non-Fock representations; 3.1 Quantum field interacting with a classical source; 3.2 Bloch-Nordsieck model; the infrared problem; 3.3 Yukawa model; non-perturbative renormalization; 4 Ultraviolet singularities and canonical quantization; 5 Problems of the interaction picture
6 Appendix: Locality and scattering6.1 Locality and asymptotic states; 6.2 Scattering by a long-range potential; 6.3 Adiabatic switching; 6.4 Asymptotic condition; 7 Wick theorem and Feynman diagrams; 7.1 Compton and electron-electron scattering; electron-positron annihilation; 3 Non-perturbative foundations of quantum field theory; 1 Quantum mechanics and relativity; 2 Properties of the vacuum correlation functions; 3 Quantum mechanics from correlation functions; 4 General properties; 4.1 Spectral condition and forward tube analyticity; 4.2 Lorentz covariance and extended analyticity
2 Euclidean invariance and symmetry3 Reflection positivity; 4 Cluster property; 5 Laplace transform condition; 6 From Euclidean to relativistic QFT; 7 Examples; 8 Functional integral representation; 6 Non-perturbative S-matrix; 1 LSZ asymptotic condition in QFT; 2 Haag-Ruelle scattering theory (massive case); 2.1 One-body problem; 2.2 Large time decay of smooth solutions; 2.3 Refined cluster property; 2.4 The asymptotic limit; 2.5 The S-matrix and asymptotic completeness; 3 Buchholz scattering theory (massless particles); 3.1 Huyghens' principle and locality; 3.2 One-body problem
International series of monographs on physics ; 158