Nonlocal Quantization Principle in Quantum Field Theory and Quantum Gravity

TL;DR

This paper proposes a nonlocal quantization approach in quantum field theory and quantum gravity, leading to damped propagators that eliminate UV divergences and extending the concept to include gravitational effects.

Contribution

It introduces a nonlocal quantization principle that modifies field operators and propagators, providing a novel way to address UV divergences in quantum theories of gravity.

Findings

Nonlocal quantization results in exponentially damped propagators.

The approach eliminates UV divergences in quantum field theory.

Extension to quantum gravity incorporates metric-dependent nonlocality.

Abstract

In this paper a nonlocal generalization of field quantization is suggested. This quantization principle presupposes the assumption that the commutator between a field operator an the operator of the canonical conjugated variable referring to other space-time points does not vanish as it is postulated in the usual setting of quantum field theory. Based on this presupposition the corresponding expressions for the field operators, the eigenstates and the path integral formula are determined. The nonlocal quantization principle also leads to a generalized propagator. If the dependence of the commutator between operators on different space-time points on the distance of these points is assumed to be described by a Gaussian function, one obtains that the propagator is damped by an exponential. This leads to a disappearance of UV divergences. The transfer of the nonlocal quantization principle to canonical quantum gravity is considered as well. In this case the commutator has to be assumed to depend also on the gravitational field, since the distance between two points depends on the metric field.