Quantum conformal symmetries for spacetimes in superposition

Viktoria Kabel; Anne-Catherine de la Hamette; Esteban Castro-Ruiz; Časlav Brukner

doi:10.22331/q-2024-12-04-1547

Quantum conformal symmetries for spacetimes in superposition

Viktoria Kabel^1,2, Anne-Catherine de la Hamette^1,2, Esteban Castro-Ruiz³, and Časlav Brukner^1,2

¹University of Vienna, Faculty of Physics, Vienna Doctoral School in Physics, and Vienna Center for Quantum Science and Technology (VCQ) , Boltzmanngasse 5, A-1090 Vienna, Austria
²Institute for Quantum Optics and Quantum Information (IQOQI), Austrian Academy of Sciences, Boltzmanngasse 3, A-1090 Vienna, Austria
³Institute for Theoretical Physics, ETH Zurich, Switzerland

Published:	2024-12-04, volume 8, page 1547
Eprint:	arXiv:2207.00021v3
Doi:	https://doi.org/10.22331/q-2024-12-04-1547
Citation:	Quantum 8, 1547 (2024).

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Abstract

Without a complete theory of quantum gravity, the question of how quantum fields and quantum particles behave in a superposition of spacetimes seems beyond the reach of theoretical and experimental investigations. Here we use an extension of the quantum reference frame formalism to address this question for the Klein-Gordon field residing on a superposition of conformally equivalent metrics. Based on the group structure of “quantum conformal transformations'', we construct an explicit quantum operator that can map states describing a quantum field on a superposition of spacetimes to states representing a quantum field with a superposition of masses on a Minkowski background. This constitutes an extended symmetry principle, namely invariance under quantum conformal transformations. The latter allows to build an understanding of superpositions of diffeomorphically non-equivalent spacetimes by relating them to a more intuitive superposition of quantum fields on curved spacetime. Furthermore, it can be used to import the phenomenon of particle production in curved spacetime to its conformally equivalent counterpart, thus revealing new features in modified Minkowski spacetime.

Featured image: A schematic pictorial representation of the situations related by a quantum conformal transformation: (1) a Klein-Gordon field with fixed mass term living on a semiclassical superposition of different conformally flat spacetimes and (2) a Klein-Gordon field with spacetime-dependent mass term in superposition on a definite flat spacetime background.

Talk by Anne-Catherine de la Hamette, Quantum Reference Frames for Superpositions of Spacetimes May 31, 2022

► BibTeX data

@article{Kabel2024quantumconformal,
  doi = {10.22331/q-2024-12-04-1547},
  url = {https://doi.org/10.22331/q-2024-12-04-1547},
  title = {Quantum conformal symmetries for spacetimes in superposition},
  author = {Kabel, Viktoria and de la Hamette, Anne-Catherine and Castro-Ruiz, Esteban and Brukner, {\v{C}}aslav},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {8},
  pages = {1547},
  month = dec,
  year = {2024}
}

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