https://doi.org/10.1140/epjc/s10052-024-12586-z
Regular Article - Theoretical Physics
On the canonical equivalence between Jordan and Einstein frames
1
Specola Vaticana (Vatican Observatory), 00120, Vatican City, Vatican City State
2
Vatican Observatory Research Group, Steward Observatory, The University of Arizona, 933 North Cherry Avenue, 85721, Tucson, AZ, USA
3
INFN, Laboratori Nazionali di Frascati, Via E. Fermi 40, 00044, Frascati, Italy
4
INAF/OAS Bologna, via Gobetti 101, 40129, Bologna, Italy
Received:
25
January
2024
Accepted:
18
February
2024
Published online:
12
March
2024
A longstanding issue is the classical equivalence between the Jordan and the Einstein frames, which is considered just a field redefinition of the metric tensor and the scalar field. In this work, based on the previous result that the Hamiltonian transformations from the Jordan to the Einstein frame are not canonical on the extended phase space, we study the possibility of the existence of canonical transformations. We show that on the reduced phase space – defined by suitable gauge fixing of the lapse and shifts functions – these transformations are Hamiltonian canonical. Poisson brackets are replaced by Dirac’s brackets following the Bergman-Dirac’s procedure. The Hamiltonian canonical transformations map solutions of the equations of motion in the Jordan frame into solutions of the equations of motion in the Einstein frame.
© The Author(s) 2024
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