Non-perturbative methods in 2 dimensional quantum field theory / Elcio Abdalla, M. Cristina B. Abdalla, Klaus D. Rothe.

Format:

Book

Author/Creator:

Abdalla, Elcio.

Contributor:

Abdalla, M. Cristina B.

Rothe, Klaus D. (Klaus Dieter)

Language:

English

Subjects (All):

Quantum field theory--Mathematical models.

Quantum field theory.

Physics.

Physical Description:

1 online resource (836 p.)

Edition:

2nd ed.

Other Title:

2 dimensional quantum field theory

Place of Publication:

Singapore ; River Edge, NJ : World Scientific, c2001.

Language Note:

English

Summary:

The second edition of Non-Perturbative Methods in Two-Dimensional Quantum Field Theory is an extensively revised version, involving major changes and additions. Although much of the material is special to two dimensions, the techniques used should prove helpful also in the development of techniques applicable in higher dimensions. In particular, the last three chapters of the book will be of direct interest to researchers wanting to work in the field of conformal field theory and strings. This book is intended for students working for their PhD degree and post-doctoral researchers wishing to a

Contents:

Contents; 1 Introduction; 2 Free Fields; 2.1 Introduction; 2.2 Bosonic Free Fields; 2.3 Fermionic Free Fields; 2.4 Bosonization of Massless Fermions; 2.5 The RS-Model; 2.6 Conclusions; 3 The Thirring model; 3.1 Introduction; 3.2 The Massless Thirring Model; 3.3 The Massive Thirring Model; 3.3.1 Equivalence with sine-Gordon equation; 3.3.2 Classical conservation laws; 3.3.3 Quantum conservation laws; 3.4 Bosonization Revisited; 3.4.1 Fermions in terms of bosons; 3.5 The Soliton as a Disorder Parameter; 3.6 Conclusion; 4 Determinants and Heat Kernels; 4.1 Introduction

4.2 Functional Determinant one-loop diagram4.2.1 Determinants and the Generalized Zeta-Function; 4.2.2 One Point Compactification; 4.2.3 The associated Dirac operator; 4.3 Calculating Seeley Coefficients; 4.3.1 The perturbative approach; 4.3.2 The Schwinger-DeWitt method; 4.3.3 The Fujikawa method; 4.4 Computing Functional Determinants; 4.4.1 C-function regularization; 4.4.2 Proper-time regularization; 4.4.3 The Fujikawa point of view; 4.5 A Theorem on a one parameter family of factorizable operators; 4.6 The QCD2 functional determinant; 4.7 Zero-modes

4.7.1 Axial anomaly equation in the presence of zero-modes4.7.2 Atiyah-Singer Index Theorem; 4.8 Ambiguities in Functional Determinants; 4.8.1 Ambiguities in the regularization; 4.8.2 Dependence on the scale parameter; 4.9 Mass expansion in proper-time regularization; 4.10 The Finite Temperature Heat Kernel; 4.10.1 Scalar held in a static background potential; 4.10.2 Scalar field in a static background gauge potential; 4.11 Conclusion; 5 Self-Interacting fermionic models; 5.1 Introduction; 5.2 The O(N) Invariant Gross-Neveu Model; 5.2.1 Classical conservation laws

5.2.2 Effective potential and B-function in a 1/N expansion5.2.3 The 1/N Expansion: Feynman rules; 5.2.4 Leading order S-matrix elements; 5.2.5 Quantization of the non-local charge; 5.3 Chiral Gross-Neveu Model; 5.3.1 Cancellation of infrared singularities; 5.3.2 The 1/N expansion; 5.3.3 Operator formulation; 5.3.4 Quantization of non-local charge; 5.4 Conclusions and Physical Interpretation; 6 Non-linear o Models: Classical Aspects; 6.1 Historical development; 6.2 Sigma models and current algebra; 6.3 Two-dimensional o models: preliminaries; 6.4 Purely Bosonic Non-linear o Models

6.4.1 Formal developments6.4.2 Dual symmetry and higher conservation laws; 6.4.3 An explicit example: the Grassmannians; 6.5 Non-linear o Models with Fermions; 6.5.1 Definition and properties; 6.5.2 Dual symmetry and higher conservation laws; 6.5.3 Construction of an explicit example; 6.6 Analogies with 4D Gauge Theories; 6.7 Concluding Remarks; 7 Non-linear o Models - Quantum Aspects; 7.1 Introduction; 7.2 Grassmannian Bosonic Models; 7.2.1 1/N expansion; 7.2.2 Renormalization; 7.2.3 Infrared divergencies; 7.2.4 Physical interpretation of the results; 7.3 Grassmannian Models and Fermions

7.3.1 1/N expansion and Feynman rules

Notes:

Description based upon print version of record.

Includes bibliographical references and index.

ISBN:

9786611951672

9781281951670

1281951676

9789812810151

9812810153