Heuristic derivation of Casimir effect in minimal length theories

TL;DR

This paper presents a heuristic method to derive the Casimir effect within minimal length theories using a Generalized Uncertainty Principle, providing corrected formulas for various geometries and discussing experimental implications.

Contribution

It introduces a heuristic derivation approach for the Casimir effect in GUP-based minimal length theories, aligning with rigorous QFT results for parallel plates.

Findings

Corrected Casimir energy formulas for parallel plates, sphere, and cylindrical shell

Consistency with quantum field theory calculations for parallel plates

Discussion on potential experimental tests of minimal length effects

Abstract

We propose a heuristic derivation of Casimir effect in the context of minimal length theories based on a Generalized Uncertainty Principle (GUP). By considering a GUP with only a quadratic term in the momentum, we compute corrections to the standard formula of Casimir energy for the parallel-plate geometry, the sphere and the cylindrical shell. For the first configuration, we show that our result is consistent with the one obtained via more rigorous calculations in Quantum Field Theory. Experimental developments are finally discussed.