Comparing formulations of generalized quantum mechanics for reparametrization - invariant systems
Mar, 199721 pages
Published in:
- Phys.Rev.D 56 (1997) 6247-6257
e-Print:
- gr-qc/9703021 [gr-qc]
Report number:
- UCSBTH-96-15,
- NSF-ITP-96-59,
- UCSBTH-96-15,
- NSF-ITP-96-59
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Abstract: (arXiv)
A class of decoherence schemes is described for implementing the principles of generalized quantum theory in reparametrization-invariant `hyperbolic' models such as minisuperspace quantum cosmology. The connection with sum-over-histories constructions is exhibited and the physical equivalence or inequivalence of different such schemes is analyzed. The discussion focuses on comparing constructions based on the Klein-Gordon product with those based on the induced (a.k.a. Rieffel, Refined Algebraic, Group Averaging, or Spectral Analysis) inner product. It is shown that the Klein-Gordon and induced products can be simply related for the models of interest. This fact is then used to establish isomorphisms between certain decoherence schemes based on these products.Note:
- 21 pages ReVTeX
- 98.80.Hw
- quantum cosmology
- quantum mechanics: decoherence
- invariance: reparametrization
- Klein-Gordon equation
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