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PreprintCC BY-NC-ND 4.0arXiv

On the quantum statistical relation and the covariant phase space Hamiltonian

  • José Luis V. Cerdeira
  • Tomás Ortín
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Abstract

We show how the covariant phase space Hamiltonian can be constructed in theories in which some of the fields have gauge freedoms. The addition to the action of boundary terms that guarantee the well-posedness of a variational principle and its exact gauge invariance for the prescribed boundary conditions turn out to be essential in this construction. The same ingredients are essential in the use of the action in the framework of Gibbons and Hawking's Euclidean approach to Quantum Gravity and we show how the on-shell action constructed with a Lagrangian with those properties can be expressed in terms of the covariant phase space Hamiltonian. We compute the Hamiltonian of several theories, one of which has Chern--Simons terms, using our prescription and show that, in black-hole backgrounds, the Hamiltonian gives directly the quantum statistical relation including terms related to non-gravitational charges and chemical potentials, as expected.

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Cite

BibTeXRIS
BibTeX
@misc{cerdeira2026quantum,
  title = {{On the quantum statistical relation and the covariant phase space Hamiltonian}},
  author = {José Luis V. Cerdeira and Tomás Ortín},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.13377},
  eprint = {2610.13377},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.13377},
  note = {CC BY-NC-ND 4.0},
}
RIS
TY  - UNPB
TI  - On the quantum statistical relation and the covariant phase space Hamiltonian
AU  - José Luis V. Cerdeira
AU  - Tomás Ortín
PY  - 2026
DA  - 2026/10/09
PB  - arXiv
DO  - 10.48550/arxiv.2610.13377
UR  - https://arxiv.org/abs/2610.13377
AB  - We show how the covariant phase space Hamiltonian can be constructed in theories in which some of the fields have gauge freedoms. The addition to the action of boundary terms that guarantee the well-posedness of a variational principle and its exact gauge invariance for the prescribed boundary conditions turn out to be essential in this construction. The same ingredients are essential in the use of the action in the framework of Gibbons and Hawking's Euclidean approach to Quantum Gravity and we show how the on-shell action constructed with a Lagrangian with those properties can be expressed in terms of the covariant phase space Hamiltonian. We compute the Hamiltonian of several theories, one of which has Chern--Simons terms, using our prescription and show that, in black-hole backgrounds, the Hamiltonian gives directly the quantum statistical relation including terms related to non-gravitational charges and chemical potentials, as expected.
ER  -