https://doi.org/10.1140/epjp/s13360-023-04731-6
Regular Article
Diamonds in Klein geometry
1
Departamento de Física, Universidade Federal de Lavras, Campus Universitário, 3037, Lavras, Minas Gerais, Brazil
2
Divisão de Astrofísica, Instituto Nacional de Pesquisas Espaciais - Inpe, São Paulo, Brazil
c
cleverson.filgueiras@ufla.br
Received:
4
November
2023
Accepted:
21
November
2023
Published online:
5
December
2023
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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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
