Probabilistic Methods in Quantum Field Theory and Quantum Gravity

1. Front Matter

   Pages i-ix

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2. Lectures

   1. Some stochastic techniques in quantization, new developments in Markov fields and quantum fields

      • Sergio Albeverio, Boguslav Zegarlinski

      Pages 1-19

   2. Random Surfaces: A Non-Perturbative Regularization of Strings?

      • Jan Ambjørn

      Pages 21-36

   3. From Lattice Gauge Theory Towards Gravity

      • Sergio Caracciolo, Andrea Pelissetto

      Pages 37-54

   4. Geometric Continuum Regularization of Quantum Field Theory

      • M. B. Halpern

      Pages 55-71

   5. Quantization = Geometry + Probability

      • John R. Klauder

      Pages 73-85

   6. Simulation of Staggered Fermions by Polymer Algorithms

      • Istvan Montvay

      Pages 87-106

   7. All Gauge Orbits and Some Gribov Copies Encompassed by the Gribov Horizon

      • Gianfausto Dell’Antonio, Daniel Zwanziger

      Pages 107-130

3. Lattice Gauge Theories

   1. Beyond the Gribov Horizon in the Femto Universe

      • Pierre van Baal

      Pages 131-152

   2. The O (N)-Symmetric Non-Linear σ-Model to Three Leading Orders in 1/N

      • Henrik Flyvbjerg, Steen Varsted

      Pages 153-166

   3. Simulations of Lattice QCD with Dynamical Fermions

      • Herbert W. Hamber

      Pages 167-182

   4. Stochastic Overrelaxation Algorithms and Critical Slowing Down

      • U. M. Heller

      Pages 183-189

   5. Slave Equations for Connected Correlation Functions

      • R. R. Horgan

      Pages 191-198

   6. The Monomer-Dimer Algorithm and QCD at Finite Density

      • Frithjof Karsch

      Pages 199-208

   7. The Theory of Hybrid Stochastic Algorithms

      • A. D. Kennedy

      Pages 209-223

   8. Numerical Investigation of Four-Dimensional Field Theories

      • Gernot Münster

      Pages 225-232

4. Quantum Gravity

   1. Probability, Time, and Gravity

      • J. Greensite

      Pages 233-242

   2. Simplicial Quantum Gravity From Two to Four Dimensions

      • Herbert W. Hamber

      Pages 243-257

   3. BRS Symmetry in Stochastic Quantization of the Gravitational Field

      • Naohito Nakazawa

      Pages 259-266

   4. Solved and Unsolved Problems in the Stochastic Quantization of Gravity

      • Helmut Rumpf

      Pages 267-277

From August 21 through August 27, 1989 the Nato Advanced Research Workshop Probabilistic Methods in Quantum Field Theory and Quantum Gravity" was held at l'Institut d'Etudes Scientifiques, Cargese, France. This publication is the Proceedings of this workshop. The purpose of the workshop was to bring together a group of scientists who have been at the forefront of the development of probabilistic methods in Quantum Field Theory and Quantum Gravity. The original thought was to put emphasis on the introduction of stochastic processes in the understanding of Euclidean Quantum Field Theory, with also some discussion of recent progress in the field of stochastic numerical methods. During the final preparation of the meeting we broadened the scope to include all those Euclidean Quantum Field Theory descriptions that make direct reference to concepts from probability theory and statistical mechanics. Several of the main contributions centered around a more rigorous discussion of stochastic processes for the formulation of Euclidean Quantum Field Theory. These rather stringent mathematical approaches were contrasted with the more heuristic stochastic quantization scheme developed in 1981 by Parisi and Wu: Stochastic quan­ tization, its intrinsic BRST -structure and stochastic regularization appeared in many disguises and in connection with several different problems throughout the workshop.

• Gravity
• field theory
• mechanics
• numerical method
• probability theory
• quantization
• quantum field
• quantum field theory
• quantum gravity
• statistical mechanics
• stochastic process

• The Niels Bohr Institute, Copenhagen, Denmark

  P. H. Damgaard

• University of Vienna, Vienna, Austria

  H. Hüffel

• Utah State University, Logan, USA

  A. Rosenblum

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