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PreprintarXiv licencearXiv

The Einstein Tensor from UV-regulated Field Correlations

  • Matheus H. Zambianco
  • Achim Kempf
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Abstract

It is known that the spacetime metric can be recovered from quantum-field correlators. We extend this programme by showing that the Einstein tensor can be directly written in terms of UV-regulated field correlations. The same correlation structure also directly determines the Ricci tensor, while higher coincidence derivatives recover the connection and Riemann tensor. We further show that the renormalized stress-energy tensor can be formulated within this framework, up to the standard finite renormalization freedom. These results provide a correlation-based organization of the semiclassical Einstein equations and advance the programme of formulating spacetime geometry in terms of quantum field correlations.

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Cite

BibTeXRIS
BibTeX
@misc{zambianco2026einstein,
  title = {{The Einstein Tensor from UV-regulated Field Correlations}},
  author = {Matheus H. Zambianco and Achim Kempf},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.05558},
  eprint = {2609.05558},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.05558},
}
RIS
TY  - UNPB
TI  - The Einstein Tensor from UV-regulated Field Correlations
AU  - Matheus H. Zambianco
AU  - Achim Kempf
PY  - 2026
DA  - 2026/09/03
PB  - arXiv
DO  - 10.48550/arxiv.2609.05558
UR  - https://arxiv.org/abs/2609.05558
AB  - It is known that the spacetime metric can be recovered from quantum-field correlators. We extend this programme by showing that the Einstein tensor can be directly written in terms of UV-regulated field correlations. The same correlation structure also directly determines the Ricci tensor, while higher coincidence derivatives recover the connection and Riemann tensor. We further show that the renormalized stress-energy tensor can be formulated within this framework, up to the standard finite renormalization freedom. These results provide a correlation-based organization of the semiclassical Einstein equations and advance the programme of formulating spacetime geometry in terms of quantum field correlations.
ER  -