New volume and inverse volume operators for loop quantum gravity

TL;DR

This paper introduces new volume and inverse volume operators in loop quantum gravity using cotriad operators, maintaining key properties and enabling anomaly-free matter Hamiltonian construction.

Contribution

It presents novel volume and inverse volume operators that preserve qualitative features and facilitate matter coupling without anomalies in loop quantum gravity.

Findings

New volume operator shares properties with standard operator

Inverse volume operator enables anomaly-free matter Hamiltonian

Potential for improved matter coupling in quantum gravity

Abstract

A new alternative volume operator is constructed for loop quantum gravity by using the so-called cotriad operators as building blocks. It is shown that the new volume operator shares the same qualitative properties with the standard volume operator. Moreover, a new alternative inverse volume operator is also constructed in the light of the construction of the alternative volume operator, which is possessed of the same qualitative properties as those of the alternative volume operator. The new inverse volume operator can be employed to construct the Hamiltonian operator of matter fields, which may lead to an anomaly-free on-shell quantum constraint algebra without any special restriction on the regularization procedure for gravity coupled to matter fields.