Quantization of simple parametrized systems
| dc.creator | Ruffini, G. | |
| dc.date | 2005-11-16 | |
| dc.date.accessioned | 2026-07-07T06:49:42Z | |
| dc.date.available | 2026-07-07T06:49:42Z | |
| dc.description | I study the canonical formulation and quantization of some simple parametrized systems, including the non-relativistic parametrized particle and the relativistic parametrized particle. Using Dirac's formalism I construct for each case the classical reduced phase space and study the dependence on the gauge fixing used. Two separate features of these systems can make this construction difficult: the actions are not invariant at the boundaries, and the constraints may have disconnected solution spaces. The relativistic particle is affected by both, while the non-relativistic particle displays only by the first. Analyzing the role of canonical transformations in the reduced phase space, I show that a change of gauge fixing is equivalent to a canonical transformation. In the relativistic case, quantization of one branch of the constraint at the time is applied and I analyze the electromagenetic backgrounds in which it is possible to quantize simultaneously both branches and still obtain a covariant unitary quantum theory. To preserve unitarity and space-time covariance, second quantization is needed unless there is no electric field. I motivate a definition of the inner product in all these cases and derive the Klein-Gordon inner product for the relativistic case. I construct phase space path integral representations for amplitudes for the BFV and the Faddeev path integrals, from which the path integrals in coordinate space (Faddeev-Popov and geometric path integrals) are derived. | |
| dc.description | 1995 UC Davis/LANL PhD thesis | |
| dc.identifier | https://arxiv.org/abs/gr-qc/0511088 | |
| dc.identifier | http://arxiv.org/abs/gr-qc/0511088 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/104452 | |
| dc.subject | General Relativity and Quantum Cosmology | |
| dc.title | Quantization of simple parametrized systems | |
| dc.type | text |