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

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