Twisted Fermionic Oscillator Algebra in $\kappa$-Minkowski space-time

TL;DR

This paper derives a twisted fermionic oscillator algebra in $$-Minkowski space-time from $$-deformed Dirac theory, revealing how noncommutative geometry modifies fermionic creation and annihilation operators.

Contribution

It introduces a novel twisted algebra for fermionic oscillators in $$-Minkowski space-time based on $$-deformed Dirac theory and the twisted flip operator.

Findings

Deformed algebra reduces to standard commutative algebra as deformation parameter approaches zero.

The work extends understanding of fermionic fields in noncommutative space-time.

Provides a framework for analyzing fermionic quantum fields in $$-deformed geometries.

Abstract

In this paper, we investigate the twisted algebra of the fermionic oscillators associated with Dirac field defined in $\kappa$-Minkowski space-time. Starting from $\kappa$-deformed Dirac theory, which is invariant under the undeformed $\kappa$-Poincare algebra, using the twisted flip operator, we derive the deformed algebra of the creation and annihilation operators corresponding to the Dirac field quanta in $\kappa$-Minkowski space-time. In the limit $a\rightarrow 0$, the deformed algebra reduces to the commutative result.