×

Loop quantum cosmology. IV: Discrete time evolution. (English) Zbl 0976.83022

Summary: Using general features of recent quantizations of the Hamiltonian constraint in loop quantum gravity and loop quantum cosmology, a dynamical interpretation of the constraint equation as evolution equation is presented. This involves a transformation from the connection to a dreibein representation and the selection of an internal time variable. Due to the discrete nature of geometrical quantities in loop quantum gravity, time also turns out to be discrete leading to a difference rather than differential evolution equation. Furthermore, evolving observables are discussed within this framework, which enables an investigation of physical spectra of geometrical quantities. In particular, the physical volume spectrum is proven to equal the discrete kinematical volume spectrum in loop quantum cosmology.
Part III, see ibid. 18, 1055-1069 (2001; Zbl 0976.83021).

MSC:

83C45 Quantization of the gravitational field
81V17 Gravitational interaction in quantum theory
83F05 Relativistic cosmology
83C05 Einstein’s equations (general structure, canonical formalism, Cauchy problems)

Citations:

Zbl 0976.83021
PDFBibTeX XMLCite
Full Text: DOI arXiv