Quantization of Fields with Constraints

1. Introduction
1.1 General
1.2 Singular Theories
2. The Structure of the Classical Singular Theory
2.1 Hamiltonian Formalism
2.2 Constraints
2.3 Theories with Second-Class Constraints
2.4 Theories with First-Class Constraints
2.5 Physical Interpretation of Degenerate Theories
2.6 Physical Quantities and Gauges in the Hamiltonian Formalism
2.7 Lagrangian Formalism, First-Class Constraints and Gauge Invariance
2.8 Formulation of a Singular Boson- and Fermion Theory in the Berezin Algebra
3. Canonical Quantization of Singular Theories
3.1 Dirac Quantization
3.2 The Generating Functional of Green Functions
3.3 Functional Integrals
3.4 Representation of the Generating Functional of Green Functions in the Form of a Functional Integral
4. Canonical Quantization of Physical Field Theories
4.1 Quantization of Electrodynamics in Canonical Gauges
4.2 Quantization of Electrodynamics in Covariant Gauges
4.2.1 Classical Consideration
4.2.2 Dirac Quantization
4.2.3 Generating Functional. Ward Identities
4.2.4 In-Limit of the Theory
4.2.5 Specification of the Physical Sector
4.3 Models with Yang-Mills Fields
4.4 Gravity
5. Lagrangian Quantization of Gauge Theories
5.1 Effective Action
5.2 Operator Formulation
5.2.1 Canonical Quantization of the Effective Yang-Mills Action
5.2.2 In-Limit
5.2.3 BRST Charge
5.2.4 Specification of the Physical Sector
6. Gauge Theories of Special Form
6.1 Structure of the Theories of Special Form
6.2 Alternative Methods of Canonical Quantization of the Theories of Special Form
6.3 Equivalence of the Definitions of Physical Functions in the Lagrangian and Hamiltonian Formalisms
7. Quantization of Singular Theories with Higher Derivatives and Theories with Time-Dependent Constraints
7.1 Theories with Higher Derivatives
7.2 Theories with Explicitly Time-Dependent Lagrangians and Constraints
7.3 Quantization of a Relativistic Particle
7.3.1 Classical Mechanics of a Relativistic Spinless Particle
7.3.2