Covariant canonical quantization of fields and Bohmian mechanics

TL;DR

This paper introduces a covariant canonical quantization method for fields using the De Donder-Weyl formulation, integrating Bohmian mechanics to maintain covariance and address quantum gravity issues.

Contribution

It develops a covariant quantization framework for fields that incorporates Bohmian mechanics, enabling a dynamic spacetime foliation and offering insights into quantum gravity.

Findings

Covariant quantization aligns with standard approaches in Minkowski spacetime.

A dynamic spacetime foliation emerges from quantum effects.

Application to quantum gravity shows advantages over Wheeler-DeWitt approach.

Abstract

We propose a manifestly covariant canonical method of field quantization based on the classical De Donder-Weyl covariant canonical formulation of field theory. Owing to covariance, the space and time arguments of fields are treated on an equal footing. To achieve both covariance and consistency with standard noncovariant canonical quantization of fields in Minkowski spacetime, it is necessary to adopt a covariant Bohmian formulation of quantum field theory. A preferred foliation of spacetime emerges dynamically owing to a purely quantum effect. The application to a simple time-reparametrization invariant system and quantum gravity is discussed and compared with the conventional noncovariant Wheeler-DeWitt approach.