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

Symmetry

IgorV. Kanatchikov¹ 

[1] School of Physics and Astronomy, University of St Andrews, St Andrews KY16 9SS, UK;

关键词: quantum field theory in curved space-time;    de donder-weyl hamiltonian formalism;    precanonical quantization;    canonical quantization;    functional schrödinger representation;   

DOI  :  10.3390/sym11111413

来源: DOAJ

【 摘 要 】

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 $\varkappa$ 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.

【 授权许可】

Unknown