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Field theoretic methods in critical phenomena with boundaries

  • A. M. Nemirovsky
Conference paper
Part of the Lecture Notes in Physics book series (LNP, volume 280)

Abstract

Recent work on field theoretic methods in critical phenomena with boundaries by the author and collaborators is described. The presence of interfaces and boundaries in critical systems produce a much richer set of phenomena than that of infinite sized systems. New universality classes are present and interesting crossover behavior occurs when there is a relative variation of additional length scales associated with either the size of the system or the boundary conditions (BC) satisfied by the order parameter on the limiting surfaces. A recently proprosed crossover renormalization group approach is very well suited to study these rich crossovers. Since functional integrals provide an indefinite integral representation of field theories, Feynman rules in configuration space are independent of geometry and BC. Renormalization of field theories with boundaries is discussed and various geometries and BC are considered. Application of field theoretic techniques are described for studying conformational properties of long polymer chains in dilute solution near interfaces or in confined domains. Also, related problems in quantum field theories with boundaries are presented.

The work I present here was performed in collaboration with K.F. Freed. Also, Z-G. Wang and J.F. Douglas have contributed to some of the work described below.

Keywords

Critical Phenomenon Feynman Rule Boundary Condition Minimal Subtraction Dimensional Crossover 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag 1987

Authors and Affiliations

  • A. M. Nemirovsky
    • 1
  1. 1.The James Franck InstituteThe University of ChicagoChicago

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