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Quantum Field Theory and Statistical Mechanics

Expositions

  • James Glimm
  • Arthur Jaffe

Table of contents

  1. Front Matter
    Pages i-vii
  2. James Glimm, Arthur Jaffe
    Pages 1-4
  3. James Glimm, Arthur Jaffe
    Pages 5-5
  4. James Glimm, Arthur Jaffe
    Pages 7-10
  5. James Glimm, Arthur Jaffe
    Pages 11-121
  6. J. Glimm, A. Jaffe
    Pages 123-179
  7. James Glimm, Arthur Jaffe
    Pages 181-199
  8. James Glimm, Arthur Jaffe
    Pages 329-347
  9. James Glimm, Arthur Jaffe, Thomas Spencer
    Pages 349-360
  10. James Glimm, Arthur Jaffe
    Pages 383-418

About this book

Introduction

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.

Keywords

algebra automorphism field field theory mechanics perturbation theory quantum field quantum field theory quantum theory relativity ring theory scattering theory special relativity statistical mechanics theory of relativity

Authors and affiliations

  • James Glimm
    • 1
  • Arthur Jaffe
    • 2
  1. 1.Courant InstituteNew YorkUSA
  2. 2.Harvard UniversityCambridgeUSA

Bibliographic information