Hamiltonian mechanics of gauge systems /
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| Author / Creator: | Prokhorov, Lev V. |
|---|---|
| Imprint: | Cambridge ; New York : Cambridge University Press, 2011. |
| Description: | xvii, 466 p. : ill. ; 26 cm. |
| Language: | English |
| Series: | Cambridge monographs on mathematical physics Cambridge monographs on mathematical physics. |
| Subject: | |
| Format: | Print Book |
| URL for this record: | http://pi.lib.uchicago.edu/1001/cat/bib/8864131 |
Table of Contents:
- Preface
- 1. Hamiltonian formalism
- 1.1. Hamilton's principle of stationary action
- 1.2. Hamiltonian equations of motion
- 1.3. The Poisson bracket
- 1.4. Canonical transformations
- 1.5. Generating functions of canonical transformations
- 1.6. Symmetries and integrals of motion
- 1.7. Lagrangian formalism for Grassmann variables
- 1.8. Hamiltonian formalism for Grassmann variables
- 1.9. Hamiltonian dynamics on supermanifolds
- 1.10. Canonical transformations on symplectic supermanifolds
- 1.11. Noether's theorem for systems on supermanifolds
- 1.12. Non-canonical transformations
- 1.13. Examples of systems with non-canonical symplectic structures
- 1.14. Some generalizations of the Hamiltonian dynamics
- 1.15. Hamiltonian mechanics. Recent developments
- 2. Hamiltonian path integrals
- 2.1. Introduction
- 2.2. Hamiltonian path integrals in quantum mechanics
- 2.3. Non-standard terms and basic equivalence rules
- 2.4. Equivalence rules
- 2.5. Rules for changing the base point
- 2.6. Canonical transformations and Hamiltonian path integrals
- 2.7. Problems with non-trivial boundary conditions
- 2.8. Quantization by the path integral method
- 3. Dynamical systems with constraints
- 3.1. Introduction
- 3.2. A general analysis of dynamical systems with constraints
- 3.3. Physical variables in systems with constraints
- 3.4. Nonlinear Poisson brackets and systems with constraints
- 4. Quantization of constrained systems
- 4.1. The Dirac method
- 4.2. The operator ordering problem in constraints
- 4.3. Relativistic particle
- 4.4. Elimination of non-physical variables. The second-class constraints
- 5. Phase space in gauge theories
- 5.1. A simple model
- 5.2. Harmonic oscillator with a conic phase space
- 5.3. The residual discrete gauge group and the choice of physical variables
- 5.4. Models with arbitrary simple compact gauge groups
- 5.5. Gauge systems with Grassmann variables
- 5.6. More general mechanical gauge systems with bosonic variables
- 5.7. Systems with Bose and Fermi degrees of freedom
- 5.8. Yang-Mills theories
- 5.9. Simple effects of the physical phase space structure in quantum theory
- 6. Path integrals in gauge theories
- 6.1. Prehminary remarks
- 6.2. Hamiltonian path integral for gauge systems with conic phase space
- 6.3. Models with more complicated structures of the physical phase space
- 6.4. Models with Grassmann variables
- 6.5. Hamiltonian path integral in an arbitrary gauge
- 6.6. Hamiltonian path integrals for gauge systems with bosons andfermions
- 6.7. The Kato-Trotter product formula for gauge theories
- 6.8. Simple consequences of the modification of the path integral for gauge systems
- 7. Confinement
- 7.1. Introduction
- 7.2. Kinematics. Gauge fields and fiber bundle theory
- 7.3. Dynamics. Quantization
- 7.4. External fields of charges and static forces. Confinement
- 8. Supplementary material
- 8.1. A brief survey of the group theory
- 8.2. Grassmann variables
- 8.3. Gaussian integrals, the Poisson summation formula, kernel Q n , and Van Fleck determinant
- 8.4. Elimination of gauge arbitrariness and residual gauge transformations
- 8.5. Gauge-invariant representations of the unit operator kernel
- References
- Index
