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Review of twisted Poincaré symmetry

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Abstract

This article reviews the construction and some applications of twisted Poincare-covariant quantum fields on the Moyal plane. The Drinfel’d twist, which plays a key mathematical role in this construction, is then applied to the case of discrete groups, with a view to applications to geons in quantum gravity. The Poincaré-twisted fields can also be applied to study the CMB anisotropies, and corrections to the power spectrum are used to put constraints on spacetime noncommutativity. The article also addresses the issue of the difference between Moyal and Voros quantum fields. Finally, it is pointed out that the Euclidean functional integrals of QFTs on the Moyal plane do not, in general, obey reflection positivity.

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Author notes

  1. A. P. Balachandran, Seckin Kürkçüoǧlu, and Sachindeo Vaidya have contributed equally to this work.

Authors and Affiliations

  1. Department of Physics, Syracuse University, Syracuse, 13244, NY, USA

    A. P. Balachandran

  2. Department of Physics, Middle East Technical University, Dumlupınar Boulevard, Ankara, 06800, Turkey

    Seckin Kürkçüoǧlu

  3. Centre for High Energy Physics, Indian Institute of Science, Bengaluru, 560012, India

    Sachindeo Vaidya

Authors
  1. A. P. Balachandran
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  2. Seckin Kürkçüoǧlu
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  3. Sachindeo Vaidya
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Corresponding author

Correspondence to Seckin Kürkçüoǧlu.

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Communicated by Guest editors: George Zoupanos, Konstantinos Anagnostopoulos, Peter Schupp.

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Balachandran, A.P., Kürkçüoǧlu, S. & Vaidya, S. Review of twisted Poincaré symmetry. Eur. Phys. J. Spec. Top. 232, 3761–3769 (2023). https://doi.org/10.1140/epjs/s11734-023-00836-2

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