Radon transform of Wheeler-De Witt equation and tomography of quantum states of the universe

Details Radon transform of Wheeler-De Witt equation and tomography of quantum states of the universe Radon transform of Wheeler-De Witt equation and tomography of quantum states of the universe

2003-07-17

arxiv.org/abs/gr-qc/0307084v2

Gen.Rel.Grav. 37 (2005) 99-114

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

22 pages LaTeX, some minor corrections, new references added, submitted to General Relativity and Gravitation

Scientific paper

10.1007/s10714-005-0005-3

The notion of standard positive probability distribution function (tomogram) which describes the quantum state of universe alternatively to wave function or to density matrix is introduced. Connection of the tomographic probability distribution with the Wigner function of the universe and with the star-product (deformation) quantization procedure is established. Using the Radon transform the Wheeler-De Witt generic equation for the probability function is written in tomographic form. Some examples of the Wheeler-DeWitt equation in the minisuperspace are elaborated explicitly for a homogeneous isotropic cosmological models. Some interpretational aspects of the probability description of the quantum state are discussed.

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