Physical States of the Quantum Conformal Factor

TL;DR

This paper investigates the quantum dynamics of the conformal factor in spacetime, revealing a spectrum of discrete states linked to Ricci scalar operators, within a canonical quantization framework on Einstein universe.

Contribution

It introduces a canonical quantization of the conformal factor affected by trace anomaly, identifying a tower of physical states satisfying quantum diffeomorphism invariance.

Findings

Discovered an infinite set of discrete quantum states.

Established a correspondence between states and Ricci scalar operators.

Demonstrated the quantization on Einstein universe.

Abstract

The conformal factor of the spacetime metric becomes dynamical due to the trace anomaly of matter fields. Its dynamics is described by an effective action which we quantize by canonical methods on the Einstein universe $R\times S^3$. We find an infinite tower of discrete states which satisfy the constraints of quantum diffeomorphism invariance. These physical states are in one-to-one correspondence with operators constructed by integrating integer powers of the Ricci scalar.