Low Dimensional Sigma Models

Overview

This book gathers together established ideas and applications of sigma models and presents them together with modern applications to provide a unified and complete view of simple sigma models and the role they play in model building in field theoretical methods in elementary particle physics.
The book is written for both mathematicians and physicists and is aimed at graduate students and researchers in theoretical particle physics who are interested in sigma models and those ...
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Overview

This book gathers together established ideas and applications of sigma models and presents them together with modern applications to provide a unified and complete view of simple sigma models and the role they play in model building in field theoretical methods in elementary particle physics.
The book is written for both mathematicians and physicists and is aimed at graduate students and researchers in theoretical particle physics who are interested in sigma models and those working in the general area of harmonic maps in pure mathematics.
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Product Details

  • ISBN-13: 9780852742310
  • Publisher: CRC Press
  • Publication date: 1/1/1989
  • Pages: 304
  • Product dimensions: 6.30 (w) x 9.30 (h) x 1.00 (d)

Table of Contents

Introduction to path integrals: Quantum mechanics. Fermions. Functional integrals in field theory. Further comments on functional methods. Green functions in field theory. Application of the saddle point method to functional integrals. Some simple calculations: Harmonic oscillator in quantum mechanics. Ground state energy. Double well potential and instantons. Role of instantons. Supersymmetric quantum mechanics. Grassmannian models and their classical solutions: Introduction - a few comments about Yang Mills theories. Grassmannian sigma-models and their instanton solutions. Properties of the solutions of the G(M,N) models. Quantum Fluctuations: The case of instantons. Noninstanton case. Sigma models with fermions: CPN-1 model with fermions. Dirac background problem. Full supersymmetric model. 1/N limits: 1/N expansion in quantum mechanics. 1/N expansion in theory. 1/N expansion of the CPN-1 model. Chiral models: Introduction. Uhlenbeck's equations and their simple solutions. Solutions of the U(4) model. General one-uniton solutions. Properties of our solutions. Sigma models with the Wess-Zumino term: Lax-pair problem. The Wess-Zumino term. U(N) model with the Wess-Zumino term. Solutions of the WZ-sigma model. Properties of the solutions. More general models: Introduction. Supersymmetric extensions. Anomaly in two-dimensions. Skyrme models: The Skyrme idea. CP1 Skyrmions. CPN-1 Skyrmions. Non-instanton solutions. The Hopf term. Appendices. References
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