Weyl frames and canonical transformations in geometrical scalar-tensor theories of gravity

TL;DR

This paper explores how Weyl transformations in scalar-tensor gravity theories act as canonical transformations in the phase space, analyzing their implications for the physical equivalence of different frames at the classical level.

Contribution

It demonstrates that Weyl transformations correspond to canonical transformations in the ADM formalism of scalar-tensor theories, providing insights into frame equivalence.

Findings

Weyl transformations induce canonical transformations in phase space.

Classical physical equivalence of different Weyl frames is discussed.

The formalism connects frame changes with phase space structure.

Abstract

We consider scalar-tensor theories of gravity defined in Weyl integrable space-time and show that in the ADM formalism Weyl transformations corresponding to change of frames induce canonical transformations between different representations of the phase space. In this context, we discuss the physical equivalence of two distinct Weyl frames at the classical level.