Quantization of set theory and generalization of the fermion algebra

Arik M., Tekin S.

JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, vol.35, no.21, pp.4591-4598, 2002 (SCI-Expanded) identifier identifier


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.