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 Quantization.- 7.3.3 A Spinning Particle.- A. Some Properties of Constraints.- B. Canonical Transformation Theorems.- C. Systems of Ordinary Differential Equations Unsolvable with Respect to the Highest Derivatives.- D. Berezin Algebra.- E. Some Properties of the Dirac Bracket.- F. Some Singular Functions.- References.- Notation.