This volume contains a selection of expository articles on quantum field theory and statistical mechanics by James Glimm and Arthur Jaffe. 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.

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 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.

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