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Open AccessArticle

Precanonical Structure of the Schrödinger Wave Functional of a Quantum Scalar Field in Curved Space-Time

1
School of Physics and Astronomy, University of St Andrews, St Andrews KY16 9SS, UK
2
National Quantum Information Center in Gdańsk (KCIK), 81-831 Sopot, Poland
Symmetry 2019, 11(11), 1413; https://doi.org/10.3390/sym11111413
Received: 20 October 2019 / Revised: 11 November 2019 / Accepted: 13 November 2019 / Published: 15 November 2019
The functional Schrödinger representation of a nonlinear scalar quantum field theory in curved space-time is shown to emerge as a singular limit from the formulation based on precanonical quantization. The previously established relationship between the functional Schrödinger representation and precanonical quantization is extended to arbitrary curved space-times. In the limiting case when the inverse of the ultraviolet parameter ϰ introduced by precanonical quantization is mapped to the infinitesimal invariant spatial volume element, the canonical functional derivative Schrödinger equation is derived from the manifestly covariant partial derivative precanonical Schrödinger equation. The Schrödinger wave functional is expressed as the trace of the multidimensional spatial product integral of Clifford-algebra-valued precanonical wave function or the product integral of a scalar function obtained from the precanonical wave function by a sequence of transformations. In non-static space-times, the transformations include a nonlocal transformation given by the time-ordered exponential of the zero-th component of spin-connection. View Full-Text
Keywords: quantum field theory in curved space-time; De Donder-Weyl Hamiltonian formalism; precanonical quantization; canonical quantization; functional Schrödinger representation quantum field theory in curved space-time; De Donder-Weyl Hamiltonian formalism; precanonical quantization; canonical quantization; functional Schrödinger representation
MDPI and ACS Style

Kanatchikov, I.V. Precanonical Structure of the Schrödinger Wave Functional of a Quantum Scalar Field in Curved Space-Time. Symmetry 2019, 11, 1413.

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