Version 1
: Received: 7 November 2019 / Approved: 8 November 2019 / Online: 8 November 2019 (11:04:19 CET)
How to cite:
Kanatchikov, I. V. Precanonical Structure of the Schrödinger Wave Functional of a Quantum Scalar Field in Curved Space-Time. Preprints2019, 2019110097. https://doi.org/10.20944/preprints201911.0097.v1
Kanatchikov, I. V. Precanonical Structure of the Schrödinger Wave Functional of a Quantum Scalar Field in Curved Space-Time. Preprints 2019, 2019110097. https://doi.org/10.20944/preprints201911.0097.v1
Kanatchikov, I. V. Precanonical Structure of the Schrödinger Wave Functional of a Quantum Scalar Field in Curved Space-Time. Preprints2019, 2019110097. https://doi.org/10.20944/preprints201911.0097.v1
APA Style
Kanatchikov, I. V. (2019). Precanonical Structure of the Schrödinger Wave Functional of a Quantum Scalar Field in Curved Space-Time. Preprints. https://doi.org/10.20944/preprints201911.0097.v1
Chicago/Turabian Style
Kanatchikov, I. V. 2019 "Precanonical Structure of the Schrödinger Wave Functional of a Quantum Scalar Field in Curved Space-Time" Preprints. https://doi.org/10.20944/preprints201911.0097.v1
Abstract
A relationship between the functional Schr\"odinger representation and the precanonical quantization of a nonlinear scalar field theory is extended to arbitrary curved space-times. The canonical functional derivative Schr\"odinger equation is derived from the manifestly covariant precanonicalSchr\"odinger equation in a singular limiting case when the ultraviolet parameter $\varkappa$ introduced by precanonical quantization is identified with the invariant delta-function at equal spatial points. In the same limiting case, the Schr\"odinger wave functional is expressed as the trace of the multidimensional product integral of Clifford-algebra-valued precanonical wave functions restricted to a certain field configuration. Thus the standard QFT in curved space-time in functional Schr\"odinger representation emerges from the precanonical formulation of quantum fields as a singular limiting case.
Keywords
quantum field theory in curved space-time; De Donder-Weyl Hamiltonian formalism; precanonical quantization; canonical quantization; functional Schrödinger representation
Subject
Physical Sciences, Quantum Science and Technology
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.