Generalizations of normal ordering and applications to quantization in classical backgrounds

TL;DR

This paper introduces a nonlocal method for extracting positive or negative frequency parts of a field, generalizing normal ordering in quantum fields within classical backgrounds, and explores implications for particle creation and cosmology.

Contribution

It presents a novel nonlocal approach to normal ordering that clarifies particle creation mechanisms in gravitational backgrounds, especially black-hole evaporation.

Findings

Reveals a hidden relation between particle current and energy-momentum tensor definitions.

Provides a local description of particle creation in black-hole evaporation.

Discusses implications for vacuum energy, dark matter, and the cosmological constant.

Abstract

A nonlocal method of extracting the positive (or the negative) frequency part of a field, based on knowledge of a 2-point function, leads to certain natural generalizations of the normal ordering of quantum fields in classical gravitational and electromagnetic backgrounds and illuminates the origin of the recently discovered nonlocalities related to a local description of particles. A local description of particle creation by gravitational backgrounds is given, with emphasis on the case of black-hole evaporation. The formalism reveals a previously hidden relation between various definitions of the particle current and those of the energy-momentum tensor. The implications to particle creation by classical backgrounds, as well as to the relation between vacuum energy, dark matter, and cosmological constant, are discussed.