Scalar Product for a Version of Minisuperspace Model with the Grassmann Variables

Sergey L. Cherkas; Vladimir L. Kalashnikov

doi:10.20944/preprints202304.0508.v1

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preprints.org > physical sciences > astronomy and astrophysics > doi: 10.20944/preprints202304.0508.v1

Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

Scalar Product for a Version of Minisuperspace Model with the Grassmann Variables

Sergey L. Cherkas

^* and

Vladimir L. Kalashnikov

Version 1 : Received: 17 April 2023 / Approved: 18 April 2023 / Online: 18 April 2023 (08:49:14 CEST)
Version 2 : Received: 2 June 2023 / Approved: 9 June 2023 / Online: 9 June 2023 (05:45:13 CEST)

A peer-reviewed article of this Preprint also exists.

Cherkas, S.L.; Kalashnikov, V.L. Scalar Product for a Version of Minisuperspace Model with Grassmann Variables. Universe 2023, 9, 508. Cherkas, S.L.; Kalashnikov, V.L. Scalar Product for a Version of Minisuperspace Model with Grassmann Variables. Universe 2023, 9, 508.

Abstract

The Grassmann variables are used to transform a system with constraints into an unconstraint system. As a result, the Schrödinger equation arises instead of the Wheeler-DeWitt one. Formally, the Schrödinger equation describes a system’s evolution, but a definition of the scalar product is needed to calculate the mean values of the operators. We suggest an explicit formula for the scalar product. The calculation of the mean values is compared with the etalon method, in which a redundant degree of freedom is excluded. Nevertheless, we could note that a complete correspondence with the etalon picture is not found. Apparently, the picture with Grassmann variables requires further search for underlying Hilbert space.

Keywords

minisuperspace model; quantum evolution; ghost variables; operator mean values

Subject

Physical Sciences, Astronomy and Astrophysics

Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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