Quantum Field Theory and Statistical Mechanics: Expositions

✍ Scribed by James Glimm, Arthur Jaffe (auth.)

• Publisher: Birkhäuser Basel
• Year: 1985
• Tongue: English
• Leaves: 405
• Edition: 1
• Category: Library

✦ Synopsis

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.

✦ Table of Contents

Front Matter....Pages i-vii
Introduction....Pages 1-4
Bibliography....Pages 5-5
Infinite Renormalization of the Hamiltonian Is Necessary....Pages 7-10
Quantum Field Theory Models....Pages 11-121
Boson Quantum Field Models....Pages 123-179
Boson Quantum Field Models....Pages 181-199
The Particle Structure of the Weakly Coupled P(φ) 2 Model and Other Applications of High Temperature Expansions....Pages 201-269
The Particle Structure of the Weakly Coupled P(φ) 2 Model and Other Applications of High Temperature Expansions....Pages 271-316
Particles and Bound States and Progress Toward Unitarity and Scaling....Pages 317-328
Critical Problems in Quantum Fields....Pages 329-347
Existence of Phase Transitions for φ 2 4 Quantum Fields....Pages 349-360
X Critical Exponents and Renormalization in the φ 4 Scaling Limit....Pages 361-382
A Tutorial Course in Constructive Field Theory....Pages 383-418

✦ Subjects

Quantum Physics;Statistical Physics, Dynamical Systems and Complexity;Field Theory and Polynomials