https://doi.org/10.1140/epjp/s13360-025-06875-z
Regular Article
New deformed boson algebra involving reflection operator and its implications to thermostatistics
1
Department of Physics and Research Institute of Natural Science, College of Natural Science, Gyeongsang National University, 660-701, Jinju, Korea
2
Department of Mechanical Engineering, Faculty of Technology, Pamukkale University, Kinikli Campus, 20160, Denizli, Türkiye
Received:
23
February
2025
Accepted:
17
September
2025
Published online:
1
October
2025
After introducing the algebraic and representative properties of the extended Weyl–Heisenberg algebra along with its special case containing the Wigner algebra, a new deformed boson algebra involving the reflection operator is proposed. Such an algebra differs from the other well-known deformed particle algebras in the literature so that its number operator spectrum constitutes a novel deformed number called 
-number, which is changed for both even n and odd n in its energy levels. As physical applications of the quantum algebra developed here, the thermostatistical properties of a gas model of the -deformed bosons and the blackbody radiation phenomena covering the -deformed photon gas are studied in detail. Another application is carried out onto lattice oscillations via the Debye crystal model containing the -deformed phonons. The effects of -deformation onto the low-temperature behavior of the model specific heat of the -deformed Debye solid are explored and are compared with the results of both the standard phonon gas and the ones with the non-extensive Tsallis statistics. Finally, possible implications of our results on other application areas of research such as strongly correlated quantum matter and star formation in cosmological systems are concisely discussed.
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2025
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.
