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

TL;DR

This paper introduces a tomographic probability distribution for the quantum state of the universe, connecting it with the Wigner function and Radon transform, and reformulates the Wheeler-De Witt equation in this framework.

Contribution

It presents a novel tomographic approach to quantum cosmology, linking probability distributions with the Wheeler-De Witt equation through Radon transform.

Findings

Established connection between tomographic distribution and Wigner function.

Reformulated Wheeler-De Witt equation in tomographic form.

Provided explicit examples for cosmological models.

Abstract

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.