Quantum Field Theory and Statistical Mechanics [electronic resource] : Expositions / by James Glimm, Arthur Jaffe
- Glimm, James
- Boston, MA : Birkhäuser Boston : Imprint: Birkhäuser, 1985.
- 1st ed. 1985.
- Physical Description:
- VII, 418 pages : online resource
- Additional Creators:
- Jaffe, Arthur, 1937- and SpringerLink (Online service)
- I Infinite Renormalization of the Hamiltonian Is Necessary -- II Quantum Field Theory Models -- I. The ?22n Model -- II. The Yukawa Model -- III Boson Quantum Field Models -- I. General Results -- II. The Solution of Two-Dimensional Boson Models -- IV Boson Quantum Field Models -- III. Further Developments -- V The Particle Structure of the Weakly Coupled P(?)2 Model and Other Applications of High Temperature Expansions -- I. Physics of Quantum Field Models -- VI The Particle Structure of the Weakly Coupled P(?)2 Model and Other Applications of High Temperature Expansions -- II. The Cluster Expansion -- VII Particles and Bound States and Progress Toward Unitarity and Scaling -- VIII Critical Problems in Quantum Fields -- IX Existence of Phase Transitions for ?24 Quantum Fields -- X Critical Exponents and Renormalization in the ?4 Scaling Limit -- Formulation of the problem -- The scaling and critical point limits -- Renormalization of the ?2(x) field -- Existence of the scaling limit -- The Josephson inequality -- XI A Tutorial Course in Constructive Field Theory -- e?tH as a functional integral -- Examples -- Applications of the functional integral representation -- Ising, Gaussian and scaling limits -- Main results -- Correlation inequalities -- Absence of even bound states -- Bound on g -- Bound on dm2/d? and particles -- The conjecture ?(6) ? 0 -- Cluster expansions -- The region of convergence -- The zeroth order expansion -- The primitive expansion -- Factorization and partial resummation -- Typical applications.
- This volume contains a selection of expository articles on quantum field theory and statistical mechanics by James Glimm and Arthur Jaffe. They include a solution of the original interacting quantum field equations and a description of the physics which these equations contain. Quantum fields were proposed in the late 1920s as the natural framework which combines quantum theory with relativ ity. They have survived ever since. The mathematical description for quantum theory starts with a Hilbert space H of state vectors. Quantum fields are linear operators on this space, which satisfy nonlinear wave equations of fundamental physics, including coupled Dirac, Max well and Yang-Mills equations. The field operators are restricted to satisfy a "locality" requirement that they commute (or anti-commute in the case of fer mions) at space-like separated points. This condition is compatible with finite propagation speed, and hence with special relativity. Asymptotically, these fields converge for large time to linear fields describing free particles. Using these ideas a scattering theory had been developed, based on the existence of local quantum fields.
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- Springer Nature eBook
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