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Diamonds in Klein geometry

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Abstract

Recently, there has been a suggestion that the Unruh effect might manifest in metamaterials at accessible Unruh temperatures. In certain instances, the class of metamaterials that could be instrumental for this observation exhibits a Klein signature instead of a Minkowski one. Consequently, confirming this effect in those materials necessitates a more meticulous analysis. In this paper, we employ the path integral formulation of Quantum Field Theory to investigate the analogue of the Unruh effect in Kleinian geometry. We perform calculations for a scalar theory, provided we restrict the action to a convenient subspace of the Kleinian spacetime. As a result, we determine the diamond temperature for a static observer with a finite lifetime. The outcome suggests that metamaterials could serve as a potential system for observing diamond regions.

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Acknowledgements

This work was partially supported by the Brazilian agencies CNPq and FAPEMIG. C. Filgueiras and L.C.T.Brito acknowledges FAPEMIG Grant No. APQ 02226/22. C. Filgueiras acknowledges CNPq Grant No. 310723/2021-3. R. M. Santos acknowledges FAPEMIG Grant No. 13681/2021-3.

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Author notes

  1. Rafael Mancini Santos

    Present address: Divisão de Astrofísica, Instituto Nacional de Pesquisas Espaciais - Inpe, São Paulo, Brazil

Authors and Affiliations

  1. Departamento de Física, Universidade Federal de Lavras, Campus Universitário, Lavras, Minas Gerais, 3037, Brazil

    Rafael Mancini Santos, L. C. T. Brito & Cleverson Filgueiras

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  1. Rafael Mancini Santos
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Correspondence to Cleverson Filgueiras.

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Santos, R.M., Brito, L.C.T. & Filgueiras, C. Diamonds in Klein geometry. Eur. Phys. J. Plus 138, 1079 (2023). https://doi.org/10.1140/epjp/s13360-023-04731-6

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