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arXiv · 2512.22958

Gravitational Noether-Ward identities for scalar field

Tomislav Prokopec
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Abstract

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.

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Tomislav Prokopec. 2025-12-28. Gravitational Noether-Ward identities for scalar field. https://arxiv.org/abs/2512.22958

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