New commutation relations for quantum gravity
Abstract
A new set of fundamental commutation relations (CR) for quantum gravity is presented. The basic variables are the eight components of the unimodular part of the spatial dreibein and eight SL(3,R) generators which correspond to Klauder's momentric variables. The commutation relations are not canonical, but they have well-defined group-theoretic meanings. Explicit unitary irreducible infinite-dimensional representations are constructed both in the metric as well as dreibein representations. The dreibein components commute among themselves; but momentric, unlike momenta, do not. This differs starkly from the usual canonical CR that allow wave functionals to be realized in either of the conjugate representations; and it may explain why our universe seems fundamentally and intuitively `metric' in nature, and not `conjugately realized'.
Cite
@article{arxiv.1601.03824,
title = {New commutation relations for quantum gravity},
author = {Chopin Soo and Hoi-Lai Yu},
journal= {arXiv preprint arXiv:1601.03824},
year = {2026}
}
Comments
6 pages. Corrected and extended. Earlier version published as `New commutation relations for quantum gravity', Chopin Soo and Hoi-Lai Yu, Chin. J. Phys. 53, 110106 (2015), Chinese Journal of Physics (Volume 53, Number 6 (November 2015)) Special Issue On the occasion of 100 years since the birth of Einstein's General Relativity