Bibliograpby . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 325 Critical point dominance in quantum field models . . . . . . . . . . . . . . . . . . . . 326 lp, ' quantum fieId model in the single-phase regioni: Differentiability of the mass and bounds on critical exponents . . . . 341 Remark on the existence of lp: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 345 On the approach to the critical point . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 348 Critical exponents and elementary...

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...

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....

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....

Describes fifteen years' work which has led to the construc- tion of solutions to non-linear relativistic local field e- quations in 2 and 3 space-time dimensions. Gives proof of the existence theorem in 2 dimensions and describes many properties of the solutions.

This IMA Volume in Mathematics and its Applications MULTIDIMENSIONAL HYPERBOLIC PROBLEMS AND COMPUTATIONS is based on the proceedings of a workshop which was an integral part ofthe 1988-89 IMA program on NONLINEAR WAVES. We are grateful to the Scientific Commit tee: James Glimm, Daniel Joseph, Barbara Keyfitz, Andrew Majda, Alan Newell, Peter Olver, David Sattinger and David Schaeffer for planning and implementing an exciting and stimulating year-long program. We especially thank the Work shop Organizers, Andrew Majda and James Glimm, for bringing together many of the major figures in a...

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....

Bibliograpby . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 325 Critical point dominance in quantum field models . . . . . . . . . . . . . . . . . . . . 326 lp, ' quantum fieId model in the single-phase regioni: Differentiability of the mass and bounds on critical exponents . . . . 341 Remark on the existence of lp: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 345 On the approach to the critical point . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 348 Critical exponents and elementary...

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....