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 .

To the Memory of Kurt Symanzik.- Monte Carlo Simulations for Quantum Field Theories Involving Fermions.- SU(2) Lattice Gauge Theory: Standard Action Versus Symanzik's Tree-Improved Action.- On-shell Improved Lattice Gauge Theories.- On the Modular Structure of Local Algebras of Observables.- The Intersection of Brownian Paths as a Case Study of a Renormalization Group Method for Quantum Field Theory.- Intersection Properties of Simple Random Walks: A Renormalization Group Approach.- Self-Avoiding Walk in 5 or More Dimensions.- Indecomposable Representations with Invariant Inner Product A Theory of the Gupta-Bleuler Triplet.- Classical Models of Confinement II.- The Energy-Momentum Spectrum in Local Field Theories with Broken Lorentz-Symmetry.- Large Deviations for Stationary Gaussian Processes.- Reduction in the Number of Coupling Parameters.- Conformal Gauges and Renormalized Equations of Motion in Massless Quantum Electrodynamics.- Longitudinal Jet Cross Sections in Order ?s2.- Convergent Perturbation Expansions for Euclidean Quantum Field Theory.- Renormalization of the Higgs Model: Minimizers, Propagators and the Stability of Mean Field Theory.