Symmetric ordering effect on Casimir energy in $\kappa-$Minkowski spacetime

TL;DR

This paper calculates the Casimir energy for a scalar field in $$-Minkowski space-time with symmetric deformation, revealing particle-antiparticle symmetry and unique deformation effects starting at order 1/κ.

Contribution

It introduces the computation of Casimir energy with symmetric deformation in $$-Minkowski space-time, highlighting differences from asymmetric cases.

Findings

Casimir energy exhibits particle-antiparticle symmetry.

Deformation effects begin at order 1/κ, unlike in parallel plates.

Symmetric deformation influences boundary condition outcomes.

Abstract

We present the Casimir energy of spherical shell, for the symmetrically deformed scalar field in $\kappa$-Minkowski space-time, satisfying Dirichlet boundary condition. The Casimir energy shows the particle anti-particle symmetry contrary to the asymmetrically deformed case. In addition, the deformation effect starts from $O(1/\kappa)$ term unlike in the parallel plates.