Gravitational Noether-Ward identities for scalar field
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866914377166225408 |
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| author | Prokopec, Tomislav |
| author_facet | Prokopec, Tomislav |
| contents | We consider the gravitational Noether-Ward identities for the evolution of general metric perturbations on quantum matter backgrounds. In this work we consider Einstein's gravity covariantly coupled to a massive, non-minimally coupled, quantum scalar field in general curved backgrounds. We find that each term in the equation of motion for gravitational perturbations satisfies its own Noether-Ward identity. Even though each term is non-transverse, the whole equation of motion maintains transversality. In particular, each counterterm needed to renormalize the graviton self-energy satisfies its own Noether identity, and we derive the explicit form for each. Finally, in order to understand how the Noether-Ward identities are affected by the definition of the metric perturbation, we consider two inequivalent definitions of metric perturbations and derive the Noether-Ward identities for both definitions. This implies that there are Noether-Ward identities for every definition of the metric perturbation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_22958 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Gravitational Noether-Ward identities for scalar field Prokopec, Tomislav General Relativity and Quantum Cosmology Cosmology and Nongalactic Astrophysics High Energy Physics - Theory We consider the gravitational Noether-Ward identities for the evolution of general metric perturbations on quantum matter backgrounds. In this work we consider Einstein's gravity covariantly coupled to a massive, non-minimally coupled, quantum scalar field in general curved backgrounds. We find that each term in the equation of motion for gravitational perturbations satisfies its own Noether-Ward identity. Even though each term is non-transverse, the whole equation of motion maintains transversality. In particular, each counterterm needed to renormalize the graviton self-energy satisfies its own Noether identity, and we derive the explicit form for each. Finally, in order to understand how the Noether-Ward identities are affected by the definition of the metric perturbation, we consider two inequivalent definitions of metric perturbations and derive the Noether-Ward identities for both definitions. This implies that there are Noether-Ward identities for every definition of the metric perturbation. |
| title | Gravitational Noether-Ward identities for scalar field |
| topic | General Relativity and Quantum Cosmology Cosmology and Nongalactic Astrophysics High Energy Physics - Theory |
| url | https://arxiv.org/abs/2512.22958 |