New deformed boson algebra involving reflection operator and its implications to thermostatistics

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 \(\nu \)-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 \(\nu \)-deformed bosons and the blackbody radiation phenomena covering the \(\nu \)-deformed photon gas are studied in detail. Another application is carried out onto lattice oscillations via the Debye crystal model containing the \(\nu \)-deformed phonons. The effects of \(\nu \)-deformation onto the low-temperature behavior of the model specific heat of the \(\nu \)-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.