Loop Quantum Cosmology II: Volume Operators

Details Loop Quantum Cosmology II: Volume Operators Loop Quantum Cosmology II: Volume Operators

1999-10-28

arxiv.org/abs/gr-qc/9910104v1

Class.Quant.Grav.17:1509-1526,2000

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

21 pages

Scientific paper

10.1088/0264-9381/17/6/313

Volume operators measuring the total volume of space in a loop quantum theory of cosmological models are constructed. In the case of models with rotational symmetry an investigation of the Higgs constraint imposed on the reduced connection variables is necessary, a complete solution of which is given for isotropic models; in this case the volume spectrum can be calculated explicitly. It is observed that the stronger the symmetry conditions are the smaller is the volume spectrum, which can be interpreted as level splitting due to broken symmetries. Some implications for quantum cosmology are presented.

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