Book contents
- Frontmatter
- Dedication
- Contents
- Preface
- Part I Special Relativity: Minkowski Space-Time
- Part II General Relativity: Globally Hyperbolic Einstein Space-Times
- Part III Dirac–Bergmann Theory of Constraints
- 8 Singular Lagrangians and Constraint Theory
- 9 Dirac Observables Invariant under the Hamiltonian Gauge Transformations Generated by First-Class Constraints
- 10 Concluding Remarks and Open Problems
- Appendix A Canonical Realizations of Lie Algebras, Poincaré Group, Poincar´e Orbits, and Wigner Boosts
- Appendix B Grassmann Variables and Pseudo–Classical Lagrangians
- Appendix C Relativistic Perfect Fluids and Covariant Thermodynamics
- References
- Index
9 - Dirac Observables Invariant under the Hamiltonian Gauge Transformations Generated by First-Class Constraints
from Part III - Dirac–Bergmann Theory of Constraints
Published online by Cambridge University Press: 17 June 2019
Book contents
- Frontmatter
- Dedication
- Contents
- Preface
- Part I Special Relativity: Minkowski Space-Time
- Part II General Relativity: Globally Hyperbolic Einstein Space-Times
- Part III Dirac–Bergmann Theory of Constraints
- 8 Singular Lagrangians and Constraint Theory
- 9 Dirac Observables Invariant under the Hamiltonian Gauge Transformations Generated by First-Class Constraints
- 10 Concluding Remarks and Open Problems
- Appendix A Canonical Realizations of Lie Algebras, Poincaré Group, Poincar´e Orbits, and Wigner Boosts
- Appendix B Grassmann Variables and Pseudo–Classical Lagrangians
- Appendix C Relativistic Perfect Fluids and Covariant Thermodynamics
- References
- Index
Summary
The method for searching the Dirac observables of a gauge theory with first- and second-class constraints based on the Shanmugadhasan canonical transformation is described. Then, for clarifying all the aspects of gauge theories there is a study of the Hessian matrix of singular Lagrangians, of the possible degenerate cases, of the equivalence of the second Noether theorem with Dirac–Bergmann theory of constraints, and of the properties of the constraints of field theories.
- Type
- Chapter
- Information
- Non-Inertial Frames and Dirac Observables in Relativity , pp. 223 - 242Publisher: Cambridge University PressPrint publication year: 2019