Collected Papers Vol.1: Quantum Field Theory and Statistical Mechanics Expositions

Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 325 Critical point dominance in quantum field models. . . . . . . . . . . . . . . . . . . . 326 q>,' quantum field model in the single-phase regions: Differentiability of the mass and bounds on critical exponents. . . . 341 Remark on the existence of q>:. . . • . . . . • . . . . • . . . . . . . . • . • . . . . . . . . . . • . 345 On the approach to the critical point . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 348 Critical exponents and elementary particles. . . . . . . . . . . . . . . . . . . . . . . . . . 362 V Particle Structure Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 371 Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 371 The entropy principle for vertex functions in quantum field models. . . . . 372 Three-particle structure of q>4 interactions and the scaling limit . . . . . . . . . 397 Two and three body equations in quantum field models. . . . . . . . . . . . . . . 409 Particles and scaling for lattice fields and Ising models. . . . . . . . . . . . . . . . 437 The resummation of one particle lines. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 450 VI Bounds on Coupling Constants Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 479 Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 479 Absolute bounds on vertices and couplings. . . . . . . . . . . . . . . . . . . . . . . . . . 480 The coupling constant in a q>4 field theory. . .. . . . . . . . . . . . . . . . . . . . . . . . 491 VII Confinement and Instantons Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 497 Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 497 Instantons in a U(I) lattice gauge theory: A coulomb dipole gas. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 498 Charges, vortices and confinement. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 516 ix VIII Reflection Positivity Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 531 Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 531 A note on reflection positivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 532 x 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.

Collected Papers — Volume 1.- I Infinite Renormalization of the Hamiltonian Is Necessary.- II Quantum Field Theory Models: Part I. The ?22n Model.- Fock space.- Q space.- The Hamiltonian H (g).- Removing the space cutoff.- Lorentz covariance and the Haag-Kastler axioms.- II. The Yukawa Model.- Preliminaries.- First and second order estimates.- Resolvent convergence and self adjointness.- The Heisenberg picture.- III Boson Quantum Field Models: Part I. General Results.- Hermite operators.- Gaussian measures and the Schrödinger representation.- Hermite expansions and Fock space.- II. The Solution of Two-Dimensional Boson Models.- The interaction Hamiltonian.- The free Hamiltonian.- Self-adjointness of H (g).- The local algebras and the Lorentz group automorphisms.- IV Boson Quantum Field Models: Part III. Further Developments.- Locally normal representations of the observables.- The construction of the physical vaccum.- Formal perturbation theory and models in three space-time dimensions.- V The Particle Structure of the Weakly Coupled P(?)2 Model and Other Applications of High Temperature Expansions: Part I. Physics of Quantum Field Models.- Five years of models.- From estimates to physics.- Bound states and resonances.- Phase space localization and renormalization.- VI The Particle Structure of the Weakly Coupled P(?)2 Model and Other Applications of High Temperature Expansions: Part II. The Cluster Expansion.- The main results.- The cluster expansion.- Clustering and analyticity: proof of the main results.- Convergence: the main ideas.- An equation of Kirkwood-Salsburg type.- Covariance operators.- Derivatives of covariance operators.- Gaussian integrals.- Convergence: the proof completed.- VII Particles and Bound States and Progess 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.