Dynamical Symmetry Breaking in Quantum Field Theories

The following sections are included:

• Preface

• Contents

The following sections are included:

• Introduction

• The Klein-Gordon Field

• The Spin- Field

• The notion of the vacuum. Nonequivalent representations of the canonical commutation relations in quantum field theory

The following sections are included:

• Introduction

• Ideal Bose Gas

• Spontaneous Symmetry Breaking in an Ideal Bose Gas

• Superfluidity. Landau Criterion

• Superfluidity in an Almost Ideal Bose Gas

• Superconductivity. General Remarks

• Ideal Fermi Gas. Fermi Gas with the Majorana Mass

• BCS Model of Superconductivity

• Dynamical U(1) Gauge Symmetry Breaking in the BCS Model

• The Ginzburg-Landau Effective Action. The Meissner Effect

The following sections are included:

• Introduction

• The Goldstone Models

• Why Do We Need the Infinite Volume for Spontaneous Symmetry Breaking?

• The Coleman Theorem and the Goldstone Theorem

• Higgs Mechanism

• Higgs Phenomenon in Non-Abelian Gauge Field Theories

• Higgs Phenomenon In Non-Abelian Gauge Field Theories. Concrete Gauges

The following sections are included:

• Introduction

• Symmetries and Currents in the Lagrangian Formalism

• Chiral Symmetry in Theory of Free Fermions

• Linear σ-Model

• The PCAC Hypothesis and the Goldberger-Treiman Relation

The following sections are included:

• Introduction

• Nonlinear Limit of the Linear σ-Model

• More on Nonlinear Chiral Theories

• Nonlinear Realization of Spontaneous Symmetry Breaking. General Theory

• Where are Nonlinear Lagrangians Useful?

The following sections are included:

• Introduction

• Dynamic Chiral Symmetry Breaking in the Nambu-Jona-Lasinio Model

• The Structure of the Vacuum in the NJL Model

• Dynamic Generation of a Majorana Mass

The following sections are included:

• Introduction

• Effective Action (Generating Functional for Proper Vertices)

• The Physical Meaning of the Effective Action

• The Loop Expansion

• One-Loop Effective Potential. Concrete Examples

• Renormalization Group Improvement of the Effective Action

• More About the Physical Meaning of the Effective Potential

The following sections are included:

• Introduction

• Effective Action for Composite Operators. The General Formalism

• The Loop Expansion for Γ(φ_c, G)

• The Two-Loop Effective Potential in the Nambu-Jona-Lasinio Model and QED

• The Schwinger-Dyson Equation and the Bethe-Salpeter Equation. General Consideration

• The Bethe-Salpeter Equation in the Nambu-Jona-Lasinio Model and QED

• Physical Interpretation of the Effective Action for Composite Operators. The Stability Criterion

The following sections are included:

• Introduction

• Chiral Ward-Takahashi Identities

• The Exact Relation for the Mass of Pseudoscalar Bosons

• The Exact Relation for the Decay Constant

• Bound States and Decay Constant in the Nambu-Jona-Lasinio Model

• Why Does the Fermion Dynamical Mass Stabilize the Vacuum?

The following sections are included:

• Introduction

• The Schwinger-Dyson Equation in the Rainbow (Ladder) Approximation in QED

• The Bethe-Salpeter Equation in Ladder QED

• The Supercritical Dynamics and the Collapse Phenomenon

• The Gauge Invariance in the Problem of Dynamical Mass Generation in QED

• The Critical Coupling Constant in Dynamical Symmetry Breaking Problem in Asymptotically Free Theories

• The Conservation Current Condition and the Proper Definition of Equations for Green's Functions. The Solution of the Goldstein Problem

• The Breakdown of Scale Symmetry in QED. Composite Operators With Large Anomalous Dimensions

• Spontaneous Chiral Symmetry Breaking in QED Beyond the Quenched Approximation

• Nonperturbative Dynamics in QED and Beyond: Miscellaneous

The following sections are included:

• Introduction

• Renormalizations and Relevant, Marginal and Irrelevant Interactions

• Transmutation of Dynamical Dimensions of Composite Operators at Strong Coupling

• Universality, Critical Exponents and Fine Tuning

• The Four-Fermion Interaction Model in D Dimensional Space-Time (2 ≤ D ≤ 4)

• Running Parameters and Renormalization of Bare Parameters. More About the Phase Transition in QED

• The Second Coleman Theorem: There Are No Goldstone Bosons in Two Dimensions

The following sections are included:

• Introduction

• Perturbative Dynamics in QCD

• The Ultraviolet Asymptotics of the Dynamical Mass Function of Quarks

• The Exact Relation for the Mass of Pseudoscalar Mesons. Hadrons Are Loose Bound States

• The Equation for the Mass Function of Quarks

• Two Scales in QCD Nonperturbative Dynamics. Dynamics Underlying Spontaneous Chiral Symmetry Breaking in QCD

• More About the Dynamics of Chiral Symmetry Breaking in QCD

• Masses of Pseudoscalar Mesons

• The Pagels-Stokar Formula for the Decay Constant

• The Low Energy Effective Action in the Extended Nambu-Jona-Lasinio Model: Preliminaries

• The Derivation of the Low Energy Effective Action in the Extended Nambu-Jona-Lasinio Model

• The Strong U₅(l) Anomaly. Effective Lagrangians Obeying the Anomalous Conservation Law

• Chiral Effective Lagrangian in QCD: General Structure and Comparison with the ENJL Model

• More About Chiral Effective Lagrangians in QCD. Naive Dimensional Analysis

• Why Are All These Models So Successful? Green's Functions of Composite Operators in QCD

The following sections are included:

• Introduction

• The Higgs Mechanism in the Standard Model

• Quarks and Leptons in the Standard Model

• Flavor-Changing Neutral Currents in the Standard Model

• The Technicolor Scenario

• Extended Technicolor

• Problems in the ETC Model Building

• The Appelquist-Carazzone Decoupling Theorem. Can One Detect the Electroweak Symmetry Breaking Mechanism in Low Energy Experiments?

• Radiative Corrections to Electroweak Interactions and Technicolor Models

The following sections are included:

• Introduction

• The Gauged Nambu-Jona-Lasinio Model as a Basic Model for New Dynamical Electroweak Symmetry Breaking Scenarios

• More About New Technicolor Models

• Nondecoupling Effects in New Technicolor Scenarios

• Tight Bound States in New Technicolor Scenarios. Bosonic Technicolor

• New Technicolor Scenarios and Lattice Computer Simulations

The following sections are included:

• Introduction

• Top Mode Standard Model

• Renormalization Group Method in the Top Mode Standard Model

• What Does the Top Mode Standard Model Explain in Electroweak Dynamics? Is it Equivalent to the Standard Model?

• Dynamical Origin of the Top Mode Standard Model

• Why is the t Quark Much Heavier Than the b Quark?

• More About Modifications of the Top Mode Standard Model

The following sections are included:

• Appendix A Dirac Equation

• Appendix B Some Useful Formulas and Relations
  • The Groups U(N)
  • Second-Order Casimir Invariant
  • Fierz Identities
  • Angle Integrations in 4-Dimensional Euclidean Space

• Appendix C Renormalization Schemes and Path Integral Representation for Green's Functions
  • Dimensional Regularization
  • Minimal Subtraction and Modified Minimal Subtraction Renormalization Schemes
  • Path Integrals

• Appendix D The Dirac Equation with the Supercritical Coulomb Potential

• Appendix E The Calculation of the Determinant of the Dirac Operator

• REFERENCES

• Subject Index