Deformed Oscillator Algebras and QFT in $\kappa$-Minkowski Spacetime

TL;DR

This paper investigates deformed oscillator algebras and quantum field theory in -Minkowski spacetime, introducing a covariant flip operator and comparing it with twisted versions, leading to new algebraic structures for quantum fields.

Contribution

It proposes a fully covariant flip operator for -Minkowski spacetime and constructs new deformed oscillator algebras, extending previous results with novel algebraic frameworks.

Findings

The covariant flip operator can be expressed in terms of Poincare9 generators to first order.

The -matrices for twisted and covariant flip operators differ at first order.

A broad class of deformed oscillator algebras is constructed, generalizing known results.

Abstract

In this paper we study the deformed statistics and oscillator algebras of quantum fields defined in $\kappa$-Minkowski spacetime. The twisted flip operator obtained from the twist associated with the star product requires an enlargement of the Poincar\'e algebra to include the dilatation generators. Here we propose a novel notion of a fully covariant flip operator and show that to the first order in the deformation parameter it can be expressed completely in terms of the Poincar\'e generators alone. The $R$-matrices corresponding to the twisted and the covariant flip operators are compared up to first order in the deformation parameter and they are shown to be different. We also construct the deformed algebra of the creation and annihilation operators that arise in the mode expansion of a scalar field in $\kappa$-Minkowski spacetime. We obtain a large class of such new deformed algebras which, for certain choice of realizations, reduce to results known in the literature.