An Enlarged Phase Space for Finite Dimensional Constrained Systems, Unifying Their Lagrangian, Phase and Velocity Space Descriptions

1990
54 pages
Published in:
  • Phys.Rept. 185 (1990) 1-54

Citations per year

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Abstract: (Elsevier)
The theory of singular Lagrangians is developed by using the second Noether theorem. The Noether identities are also obtained in the presence of second-class constraints and compared with the Dirac-Bergmann algorithm in phase space ( T ∗ Q ). The true gauge transformations are those Noether transformations which satisfy the Jacobi equation and an open gauge algebra every time they are velocity dependent. The velocity-space ( TQ ) description is made: the extra gauge symmetries in TQ are connected with local dynamical symmetries of the Euler-Lagrange equations. Then the T ∗ ( TQ ) description is developed and the associated path integral defined: it allows the measure for the TQ path integral to be found and is locally connected with the standard T ∗ Q one. The canonical quantization of first-class constraints is done without introducing gauge fixings by means of the “multitemporal approach”, which was developed for relativistic particle mechanics.
  • review
  • quantization: constraint
  • quantum mechanics
  • transformation: gauge
  • path integral
  • bibliography