Quantization of set theory and generalization of the fermion algebra

Abstract

Summary: The quantum states of a \(d\)-dimensional fermion algebra are in one to one correspondence with the subsets of a \(d\)-element universal set. In this paper we use this set theoretical motivation to construct a one-parameter deformation of the fermion algebra and extend it to a \(d\)-dimensional generalization which is invariant under the group \(U(d)\). This discrete fermionic oscillator system is extended to the continuous case. We also show that the \(q\)-deformation of these systems is related to supercovariant \(q\)-oscillators.