Quantum Mechanical Breaking of Local GL(4) Invariance
R. Floreanini, R. Percacci
TL;DR
This paper investigates how quantum effects break local GL(4) invariance in a reformulation of General Relativity coupled with a scalar field, revealing that quantum corrections favor a specific vierbein configuration.
Contribution
It demonstrates that quantum one-loop corrections break the classical local GL(4) invariance in a scalar-coupled gravity model, identifying the effective potential's minima.
Findings
Quantum corrections break GL(4) invariance.
Minima occur for a vierbein proportional to the identity.
Quantum effects select a preferred vierbein configuration.
Abstract
We consider the gravitational coupling of a scalar field, in a reformulation of General Relativity exhibiting local GL(4) invariance at the classical level. We compute the one-loop contribution of the scalar to the quantum effective potential of the vierbein and find that it does not have GL(4) invariance. The minima of the effective potential occur for a vierbein which is proportional to the unit matrix.
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