Research Catalog

Title

Critical properties of [Greek letter phi]⁴-theories / Hagen Kleinert, Verena Schulte-Frohlinde.

Author

Kleinert, Hagen

Publication

River Edge, N.J. : World Scientific, c2001.

Items in the Library & Off-site

Details

Additional Authors

Schulte-Frohlinde, Verena

Description

xx, 489 p. : ill.; 27 cm.

Summary

"This book explains in detail how to perform perturbation expansions in quantum field theory to high orders, and how to extract the critical properties of the theory from the resulting divergent power series. These properties are calculated for various second-order phase transitions of three-dimensional systems with high accuracy, in particular the critical exponents observable in experiments close to the phase transition." "The [phi][superscript 4]-theories investigated in this book contain any number N of fields in an O(N)-symmetric interaction, or in an interaction in which O(N)-symmetry is broken by a term of a cubic symmetry. The crossover behavior between the different symmetries is investigated. In addition, alternative ways of obtaining critical exponents of [phi][superscript 4]-theories are sketched, such as variational perturbation expansions in three rather than 4-[epsilon] dimensions, and improved ratio tests in high-temperature expansions of lattice models." "Readership: Graduate students, researchers and academics/lecturers in theoretical physics."--Jacket.

Subject

• Perturbation (Quantum dynamics)

Bibliography (note)

• Includes bibliographical references and index.

Processing Action (note)

• committed to retain

Contents

Second-Order Phase Transitions -- Critical Exponents -- Models for Critical Behavior -- Fluctuating Fields -- Correlations and Structure Factor -- Definition of phi[superscript 4]-Theory -- Partition Function and Generating Functional -- Free-Field Theory -- Perturbation Expansion -- Composite Fields -- Feynman Diagrams -- Diagrammatic Expansion of Correlation Functions -- Diagrammatic Expansion of the Partition Function -- Connected and Disconnected Diagrams -- Connected Diagrams for Two- and Four-Point Functions -- Diagrams for Composite Fields -- Diagrams in Momentum Space -- Fourier Transformation -- One-Particle Irreducible Diagrams and Proper Vertex Functions -- Composite Fields -- Theory in Continuous Dimension D -- Structural Properties of Perturbation Theory -- Generating Functionals -- Connectedness Structure of Correlation Functions -- Decomposition of Correlation Functions into Connected Correlation Functions -- Functional Generation of Vacuum Diagrams -- Correlation Functions From Vacuum Diagrams -- Generating Functional for Vertex Functions -- Landau Approximation to Generating Functional -- Composite Fields -- Diagrams for Multicomponent Fields -- Interactions with O(N) Cubic Symmetry -- Free Generating Functional for N Fields -- Perturbation Expansion for N Fields and Symmetry Factors -- Symmetry Factors -- Scale Transformations of Fields and Correlation Functions -- Free Massless Fields -- Free Massive Fields -- Interacting Fields -- Anomaly in the Ward Identities -- Regularization of Feynman Integrals.

ISBN

• 9810246587
• 9810246595 (pbk.)

LCCN

^^2001280526

OCLC

• 48491238
• SCSB-10084124

Owning Institutions

Harvard Library