Symplectic method in quantum cosmology
Abstract
In the present work, we study the quantum cosmology description of Friedmann-Robertson-Walker models in the presence of a generic perfect fluid and a cosmological constant, which may be positive or negative. We work in Schutz’s variational formalism and the three-dimensional spatial sections may have positive, negative, or zero constant curvature. If one uses the scale factor and its canonically conjugated momentum as the phase space variables that describe the geometrical sector of these models, one obtains Wheeler-DeWitt equations with operator ordering ambiguities. In order to avoid those ambiguities and simplify the quantum treatment of the models, we follow references [Edésio M. Barbosa, Jr. and Nivaldo A. Lemos, Gen. Relativ. Gravit. 38, 1609 (2006).GRGVA80001-770110.1007/s10714-006-0333-y][Edésio M. Barbosa, Jr. and Nivaldo A. Lemos, Phys. Rev. DPRVDAQ1550-7998 78, 023504 (2008).10.1103/PhysRevD.78.023504] and introduce new phase space variables. We explicitly demonstrate, using the symplectic method, that the transformation leading from the old set of variables to the new one is canonical.
- Publication:
-
Physical Review D
- Pub Date:
- August 2009
- DOI:
- 10.1103/PhysRevD.80.047302
- arXiv:
- arXiv:0903.3933
- Bibcode:
- 2009PhRvD..80d7302S
- Keywords:
-
- 98.80.Qc;
- 04.40.Nr;
- 04.60.Ds;
- Quantum cosmology;
- Einstein-Maxwell spacetimes spacetimes with fluids radiation or classical fields;
- Canonical quantization;
- General Relativity and Quantum Cosmology
- E-Print:
- Revtex4, 18 pages, 2 EPS figures