"Gauge" freedom and relationship between the Einstein and Jordan conformal frames

TL;DR

This paper examines the physical equivalence of Einstein and Jordan conformal frames in Jordan-Brans-Dicke theory, highlighting how gauge choices affect conformal invariance and clarifying related conceptual issues.

Contribution

It clarifies the role of gauge fixing in the conformal transformation between Einstein and Jordan frames, addressing misconceptions about their physical equivalence.

Findings

Equations are not invariant under conformal transformations with the same gauge fixing.

Gauge choices influence the perceived equivalence of the frames.

The paper clarifies conceptual ambiguities in conformal invariance in scalar-tensor theories.

Abstract

The issue of the physical equivalence between the Einstein and Jordan conformal frames in Jordan-Brans-Dicke (JBD) theory is revised. Scalar-tensor theories equations are not invariant with respect to conformal transformations if one uses the same "gauge" fixing in Jordan and Einstein frames. We hope to have clarified some eventual obscure issues associated to the concept of conformal invariance of relativistic theories appearing in the literature, in particular the relationship between Jordan and Einstein frames.