https://doi.org/10.1140/epjc/s10052-024-12677-x
Regular Article - Theoretical Physics
Dirac–Bergmann analysis and degrees of freedom of coincident f(Q)-gravity
1
Department of Physics, Tokyo Institute of Technology, 2-12-1 Ookayama, Meguro-ku, 152-8551, Tokyo, Japan
2
Kavli Institute for the Physics and Mathematics of the Universe (Kavli IPMU), The University of Tolyo, 5-1-5 Kashiwanoha, Kashiwa, 277-8583, Chiba, Japan
a tomonari.k.aa@m.titech.ac.jp, ktomonari.phys@gmail.com
Received:
4
January
2024
Accepted:
13
March
2024
Published online:
3
April
2024
We investigate the propagating degrees of freedom of f(Q)-gravity in a 4-dimensional space-time under the imposition of the coincident gauge by performing the Dirac–Bergmann analysis. In this work, we start with a top-down reconstruction of the metric-affine gauge theory of gravity based only on the concept of a vector bundle. Then, the so-called geometrical trinity of gravity is introduced and the role of the coincident GR is clarified. After that, we reveal relationships between the boundary terms in the variational principle and the symplectic structure of the theory in order to confirm the validity of the analysis for our studied theories. Then, as examples, we revisit the analysis of GR and its 
-extensions. Finally, after reviewing the Dirac–Bergmann analysis of the coincident GR and that of f(T)-gravity, we perform the analysis of coincident f(Q)-gravity. Under the imposition of appropriate spatial boundary conditions, we find that, as a generic case, the theory has five primary, three secondary, and two tertiary constraint densities and all these constraint densities are classified into second-class constraint density; the number six is the propagating degrees of freedom of the theory and there are no longer any remaining gauge degrees of freedom. We also discuss the condition of providing seven pDoF as a generic case. The violation of diffeomorphism invariance of coincident f(Q)-gravity make it possible to emerge such several sectors.
An erratum to this article is available online at https://doi.org/10.1140/epjc/s10052-024-12813-7.
© The Author(s) 2024
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
Funded by SCOAP3.
