Scale limited fields and the Casimir effect

TL;DR

This paper explores the Casimir effect using wavelet-based scale limitations on quantum fields, analyzing how resolution restrictions influence the force between plates under various boundary conditions.

Contribution

It introduces a wavelet transform approach to incorporate scale limitations in Casimir effect calculations, providing new insights into resolution-dependent quantum phenomena.

Findings

Casimir force depends on wavelet choice and scale cutoff size.

Wavelet-based scale restriction models observational and fundamental resolution limits.

Results vary with boundary conditions and wavelet types.

Abstract

We revisit the calculation of the Casimir effect from the perspective of scale limited resolutions of quantum fields. We use the continuous wavelet transform to introduce a scale degree of freedom and then restrict it to simulate either an observational or fundamental limitation of resolution. The Casimir force is derived in this setting for a free complex massless scalar field between two infinite plates with both Dirichlet and periodic boundary conditions. The dependence of the force on the choice of wavelet and size of scale cutoff is extensively discussed for several examples of wavelets.