Renormalization of quantum field theories with non-linear field transformations proceedings of a workshop, held at Ringberg Castle, Tegernsee, FRG, February 16 - 20, 1987

The characteristic feature of many models for field theories based on concepts of differential geometry is their nonlinearity. In this book a systematic exposition of nonlinear transformations in quantum field theory is given. The book starts with a short account of the renormalization theory with examples which can be handled successfully in four space-time dimensions. The second part is devoted to nonlinear sigma-models and their constructions in two dimensions. In the final section geometrical and cohomological methods and the relations to string theory are treated. This book is an important contribution towards rigorous definitions, and the mastering of nonlinear reparametrizations in agreement with the principles of quantum field theory will help to deal with anomalies, geometry and the like consistently and thus to understand better their implications for physics. The collection of papers addresses researchers and graduate students as well and will stimulate further work on the foundations of quantum field theory. Renormalization theory, a short account of results and problems....Pages 1-21 Some remarks for the construction of yang-mills field theories....Pages 22-31 Non-linear field transformations simple examples and general remarks....Pages 32-44 Superspace renormalization of N = 1, d = 4 supersymmetric gauge theories....Pages 45-63 N = 2 Supersymmetric Yang-Mills Theories in the Wess-Zumino Gauge....Pages 64-80 Radiative mass generation in scale invariant systems with spontaneous symmetry breakdown....Pages 81-92 Discussion session on part I: Non-linear field transformations in 4 dimensions....Pages 93-94 The non-linear sigma model....Pages 95-108 B.R.S. renormalization of B(n+1) non linear δ-model....Pages 109-119 Renormalization of bosonic non-linear δ-models built on compact homogeneous manifolds....Pages 120-129 Nonlinear field renormalizations in the background field method....Pages 130-143 Kahler geometry and supersymmetric non-linear σ-models: An introduction....Pages 144-150 Methods in hyperkähler σ models building....Pages 151-159 Sigma model β-functions at all loop orders....Pages 160-169 The d=2 conformally invariant SU(2) σ-model with wess-zumino term and related critical theories +) ....Pages 170-178 The two-dimensional 0(n) nonlinear σ-model from a wilson renormalization group viewpoint....Pages 179-196 Nonlinear δ-models with boundary and open strings....Pages 197-208 Discussion session on part II: Non-linear σ-models....Pages 209-212 Remarks on slavnov symmetries....Pages 213-219 Supersymmetric properties of field theories in 10-D....Pages 220-231 Generalized wess-zumino terms....Pages 232-239 Contents: Non-linear Field Transformations in Four Dimensions: Contributions by P. Breitenlohner, R. Collina, D. Maison, O. Piguet, R. Sénéor, K. Sibold Non-linear -Models: Contributions by C. Becchi, A. Blasi, G. Bonneau, H. Dorn, R. Flume, P. Mitter, D. Olivier, C. Pope, K. Stelle Cohomological and Geometrical Methods, Relation to String Theory: Contributions by L. Bonora, M. Bregola, P. Cotta-Ramusino, K. Lechner, P. Pasti, M. Rimaldi, R. Stora, M. Tonin.