Working Paper Article Version 1 This version is not peer-reviewed

The tomographic Wheeler De Witt equation

Version 1 : Received: 1 February 2021 / Approved: 2 February 2021 / Online: 2 February 2021 (08:28:59 CET)

How to cite: Stornaiolo, C. The tomographic Wheeler De Witt equation. Preprints 2021, 2021020076 Stornaiolo, C. The tomographic Wheeler De Witt equation. Preprints 2021, 2021020076

Abstract

Recently quantum cosmology in tomographic representation was considered. as an important tool to analyze the quantum states of the early universe in relation with the subsequent classical evolution. Given a wave function the correspondent tomogram is defined proportional to the square modulus of its fractional Fourier transform. The classical limit obtained by taking the limit ℏ→0 can be compared with the classical tomogram obtained from the classical hamiltonian formalism. In this paper we show that a set of tomograms can be derived as exact solutions of a third order equation when a de Sitter quantum universe is considered. We finally discuss the limits of this approach to quantum cosmology because the extension to equations with arbitrary potentials can become extremely complicated for potentials given by algebraic polynomials of degree greater than two and therefore also for potentials expressible by arbitrary functions.

Subject Areas

Quantum cosmology; symplectic tomography; cosmology

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