Representations of relativity, quantum gravity and cosmology

TL;DR

This paper reviews a canonical approach to quantum gravity, extending spacetime to momentum-energy space, and discusses how noninertial frames introduce new dynamics affecting quantization consistency.

Contribution

It proposes a foundational principle for quantum gravity based on extending relativistic postulates to momentum-energy space, enabling consistent canonical quantization.

Findings

Extension to noninertial frames introduces a new dynamical field.

The approach allows for hermitian operator ordering in quantum gravity.

Provides a framework for consistent quantization of gravity.

Abstract

We review an attempt to set a suitable foundational principle for consistent quantization of gravity based on the canonical formulation. It requires extending the spacetime description of the relativistic postulates to also encompass an alternative formulation in momentum-energy continuum where the inertial physical laws can be equivalently described. The extension to noninertial frames breaks such an equivalence, leaving a new dynamical field which, together with gravity, allows to construct a canonical scenario where the Dirac's quantization method leads to consistent definitions of hermitian ordering for the operators of the canonical quantum theory.