On the canonical equivalence between Jordan and Einstein frames
Abstract 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 Einst...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2024-03-01
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| Series: | European Physical Journal C: Particles and Fields |
| Online Access: | https://doi.org/10.1140/epjc/s10052-024-12586-z |
| _version_ | 1797259107985522688 |
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| author | Gabriele Gionti Matteo Galaverni |
| author_facet | Gabriele Gionti Matteo Galaverni |
| author_sort | Gabriele Gionti |
| collection | DOAJ |
| description | Abstract 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. |
| first_indexed | 2024-04-24T23:04:11Z |
| format | Article |
| id | doaj.art-d7b90dec474e41319ed0bb91167388ef |
| institution | Directory Open Access Journal |
| issn | 1434-6052 |
| language | English |
| last_indexed | 2024-04-24T23:04:11Z |
| publishDate | 2024-03-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | European Physical Journal C: Particles and Fields |
| spelling | doaj.art-d7b90dec474e41319ed0bb91167388ef2024-03-17T12:36:03ZengSpringerOpenEuropean Physical Journal C: Particles and Fields1434-60522024-03-0184311810.1140/epjc/s10052-024-12586-zOn the canonical equivalence between Jordan and Einstein framesGabriele Gionti0Matteo Galaverni1Specola Vaticana (Vatican Observatory)Specola Vaticana (Vatican Observatory)Abstract 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.https://doi.org/10.1140/epjc/s10052-024-12586-z |
| spellingShingle | Gabriele Gionti Matteo Galaverni On the canonical equivalence between Jordan and Einstein frames European Physical Journal C: Particles and Fields |
| title | On the canonical equivalence between Jordan and Einstein frames |
| title_full | On the canonical equivalence between Jordan and Einstein frames |
| title_fullStr | On the canonical equivalence between Jordan and Einstein frames |
| title_full_unstemmed | On the canonical equivalence between Jordan and Einstein frames |
| title_short | On the canonical equivalence between Jordan and Einstein frames |
| title_sort | on the canonical equivalence between jordan and einstein frames |
| url | https://doi.org/10.1140/epjc/s10052-024-12586-z |
| work_keys_str_mv | AT gabrielegionti onthecanonicalequivalencebetweenjordanandeinsteinframes AT matteogalaverni onthecanonicalequivalencebetweenjordanandeinsteinframes |