https://doi.org/10.1140/epjs/s11734-023-00836-2
Review
Review of twisted Poincaré symmetry
1
Department of Physics, Syracuse University, 13244, Syracuse, NY, USA
2
Department of Physics, Middle East Technical University, Dumlupınar Boulevard, 06800, Ankara, Turkey
3
Centre for High Energy Physics, Indian Institute of Science, 560012, Bengaluru, India
Received:
19
May
2022
Accepted:
14
April
2023
Published online:
14
June
2023
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.
A. P. Balachandran, Seckin Kürkçüoǧlu, and Sachindeo Vaidya have contributed equally to this work.
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