Polynomial algebra with reflection symmetry and thermostatistics

Abstract

In this paper, we use the reflection (or parity) operator to construct the new algebra whose maximum occupation number is finite. For the Hamiltonian proportional to the number operator, we discuss the thermostatistics and compute the thermodynamical quantities such as distribution function, multiparticle distribution function, mean energy and specific heat. We also calculate the intercept for this algebra to show that a particle obeying this algebra is an exotic particle which is neither a boson nor a fermion.