Invariance quantum group of the fermionic oscillator

TL;DR

This paper investigates the symmetry properties of the fermionic oscillator, revealing that its invariance group extends from a classical group to a quantum group, highlighting a novel quantum symmetry structure.

Contribution

It demonstrates that the inhomogeneous invariance group of the fermionic oscillator is a quantum group, extending classical symmetry analysis to quantum algebraic structures.

Findings

The fermionic oscillator's invariance group is a quantum group.

The classical invariance group is O(2).

The inhomogeneous invariance group is a quantum extension.

Abstract

The fermionic oscillator defined by the algebraic relations cc^*+c^*c=1 and c^{2}=0 admits the homogeneous group O(2) as its invariance group. We show that, the structure of the inhomogeneous invariance group of this oscillator is a quantum group.