Quantum Field Theory : A Selection of Papers in Memoriam Kurt Symanzik

Kurt Symanzik was certainly one of the most outstanding theoretical physicists of our time. For thirty years, until his untimely death in 1983, he helped to shape the present form of quantum field theory and its application to elementary particle physics. In memoriam of Kurt" Symanzik leading scientists present their most recent results, giving, at the same time, an overview of the state of the art. This collection was originally published in Vol. 97, 1/2 (1985) of Communications in Mathematical Physics. They range over various inter­ related topics of interest to Kurt Symanzik. We hope that making this collection available in an accessible and inexpensive way will benefit the physics community. The Publisher Contents To the Memory of Kurt Symanzik 1 By A. Jaffe, H. Lehmann, and G. Mack Monte Carlo Simulations for Quantum Field Theories Involving Fermions. By M. Karowski, R. Schrader, and H. J. Thun (With 8 Figures) . . . . . . . . . . . . . . . . . . . 5 SU(2) Lattice Gauge Theory: Standard Action Versus Symanzik's Tree-Improved Action. By B. Berg, A. Billoire, S. Meyer, and C. Panagiotakopoulos (With 13 Figures). . . . . . . . . . 31 . On-shell Improved Lattice Gauge Theories By M. Luscher and P. Weisz (With 3 Figures) . . . . . 59 On the Modular Structure of Local Algebras of Observables By K. Fredenhagen . . . . . . . . . . . . . . . . . 79 . . . The Intersection of Brownian Paths as a Case Study of a Renormalization Group Method for Quantum Field Theory By M. Aizenman (With 3 Figures). . . . . . . . . . . . 91 Intersection Properties of Simple Random Walks: A Renormalization Group Approach. By G. Felder and J. Frohlich. . . . . . . 111 . Front Matter....Pages I-VIII Kurt Symanzik....Pages 1-1 Monte Carlo Simulations for Quantum Field Theories Involving Fermions....Pages 5-29 SU(2) Lattice Gauge Theory: Standard Action Versus Symanzik’s Tree-Improved Action....Pages 31-58 On-shell Improved Lattice Gauge Theories....Pages 59-77 On the Modular Structure of Local Algebras of Observables....Pages 79-89 The Intersection of Brownian Paths as a Case Study of a Renormalization Group Method for Quantum Field Theory....Pages 91-110 Intersection Properties of Simple Random Walks: A Renormalization Group Approach....Pages 111-124 Self-Avoiding Walk in 5 or More Dimensions....Pages 125-148 Indecomposable Representations with Invariant Inner Product....Pages 149-159 Classical Models of Confinement II....Pages 161-167 The Energy-Momentum Spectrum in Local Field Theories with Broken Lorentz-Symmetry....Pages 169-185 Large Deviations for Stationary Gaussian Processes....Pages 187-210 Reduction in the Number of Coupling Parameters....Pages 211-225 Conformal Gauges and Renormalized Equations of Motion in Massless Quantum Electrodynamics....Pages 227-255 Longitudinal Jet Cross Sections in Order α s 2 ....Pages 257-266 Convergent Perturbation Expansions for Euclidean Quantum Field Theory....Pages 267-298 Renormalization of the Higgs Model: Minimizers, Propagators and the Stability of Mean Field Theory....Pages 299-329