Classical and quantum dynamics of constrained Hamiltonian systems

Classical and quantum dynamics of constrained Hamiltonian systems / Heinz J Rothe & Klaus D Rothe.

This book is an introduction to the field of constrained Hamiltonian systems and their quantization, a topic which is of central interest to theoretical physicists who wish to obtain a deeper understanding of the quantization of gauge theories, such as describing the fundamental interactions in natu...

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Bibliographic Details
Main Author: Rothe, Heinz J.
Other Authors: Rothe, Klaus D. (Klaus Dieter)
Format: eBook
Language:English
Published: New Jersey : World Scientific, ©2010.
Series:World Scientific lecture notes in physics ; v. 81.
Subjects:
Quantum theory.
Hamiltonian systems.
Constraints (Physics)
Gauge fields (Physics)
Mathematical physics.
SCIENCE > Physics > Quantum Theory.
Hamiltonian systems
Mathematical physics
Quantum theory
Online Access:Click for online access
Table of Contents:
  • 1. Introduction
  • 2. Singular Lagrangians and local symmetries. 2.1. Introduction. 2.2. Singular Lagrangians. 2.3. Algorithm for detecting local symmetries on Lagrangian level. 2.4. Examples. 2.5. Generator of gauge transformations and Noether identities
  • 3. Hamiltonian approach. The Dirac formalism. 3.1. Introduction. 3.2. Primary constraints. 3.3. The Hamilton equations of motion. 3.4. Iterative procedure for generating the constraints. 3.5. First and second class constraints. Dirac brackets
  • 4. Symplectic Approach to constrained systems. 4.1. Introduction. 4.2. The case f[symbol] singular. 4.3. Interpretation of W[symbol] and F. 4.4. The Faddeev-Jackiw reduction
  • 5. Local symmetries within the Dirac formalism. 5.1. Introduction. 5.2. Local symmetries and canonical transformations. 5.3. Local symmetries of the Hamilton equations of motion. 5.4. Local symmetries of the total and extended action. 5.5. Local symmetries of the Lagrangian action. 5.6. Solution of the recursive relations. 5.7. Reparametrization invariant approach
  • 6. The Dirac conjecture. 6.1. Introduction. 6.2. Gauge identities and Dirac's conjecture. 6.3. General system with two primaries and one secondary constraint. 6.4. Counterexamples to Dirac's conjecture?
  • 7. BFT embedding of second class systems. 7.1. Introduction. 7.2. Summary of the BFT-procedure. 7.3. The BFT construction. 7.4. Examples of BFT embedding
  • 8. Hamilton-Jacobi theory of constrained systems. 8.1. Introduction. 8.2. HJ equations for first class systems. 8.3. HJ equations for second class systems
  • 9. Operator quantization of second class systems. 9.1. Introduction. 9.2. Systems with only second class constraints. 9.3. Systems with first and second class constraints
  • 10. Functional quantization of second class systems. 10.1. Introduction. 10.2. Partition function for second class systems
  • 11. Dynamical gauges. BFV functional quantization. 11.1. Introduction. 11.2. Grassmann variables. 11.3. BFV quantization of a quantum mechanical model. 11.4. Quantization of Yang-Mills theory in the Lorentz gauge. 11.5. Axiomatic BRST approach. 11.6. Equivalence of the SD and MCS models. 11.7. The physical Hilbert space. Some remarks
  • 12. Field-antifield quantization. 12.1. Introduction. 12.2. Axiomatic field-antifield formalism. 12.3. Constructive proof of the field-antifield formalism for a restricted class of theories. 12.4. The Lagrangian master equation. 12.5. The quantum master equation. 12.6. Anomalous gauge theories. The chiral Schwinger model
  • A. Local symmetries and singular Lagrangians. A.1. Local symmetry transformations. A.2. Bianchi identities and singular Lagrangians
  • B. The BRST charge of rank one
  • C. BRST Hamiltonian of rank one
  • D. The FV principal theorem
  • E. BRST quantization of SU(3) Yang-Mills theory in [symbol]-gauges.

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