q-DEFORMED FERMION OSCILLATORS, ZERO-POINT ENERGY AND INCLUSION-EXCLUSION PRINCIPLE

The theory of Fermion oscillators has two essential ingredients: zero-point energy and Pauli exclusion principle. We devlop the theory of the statistical mechanics of generalized q-deformed Fermion oscillator algebra with inclusion principle (i.e., without the exclusion principle), which corresponds to ordinary fermions with Pauli exclusion principle in the classical limit q → 1. Some of the remarkable properties of this theory play a crucial role in the understanding of the q-deformed Fermions. We show that if we insist on the weak exclusion principle, then the theory has the expected low temperature limit as well as the correct classical q-limit. PACS numbers: 05.30.-d, 05.70.-Cd, 05.70.-Fh, 05.90.+m Preprint SIUE/HEP-1/ 1999 Let us begin with the classical system of ordinary quantum Fermion harmonic oscillators with the spectrum En = (n− 1 2 )h̄ω, n = 0, 1 , (1) and the Partition function given by Z = 1