Abstract
The notion of standard positive probability distribution function (tomogram) which describes the quantum state of the universe alternatively to the wave function or to the 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 homogeneous isotropic cosmological models. Some interpretational aspects of the probability description of the quantum state are discussed.
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Man’ko, V.I., Marmo, G. & Stornaiolo, C. Radon transform of the Wheeler-De Witt equation and tomography of quantum states of the universe. Gen Relativ Gravit 37, 99–114 (2005). https://doi.org/10.1007/s10714-005-0005-3
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DOI: https://doi.org/10.1007/s10714-005-0005-3