Casimir interactions from infinite range and dilation symmetry

TL;DR

This paper investigates Casimir interactions in self-similar configurations of parallel plates and a scalar field model, revealing attraction at infinite range and linking it to self-similarity in statistical fields.

Contribution

It introduces a novel analysis of Casimir energies in self-similar systems and connects these phenomena to infinite-range fluctuations in scalar field models.

Findings

Attractive Casimir force characteristics emerge only at infinite range.

Casimir-like energy appears in a Gaussian Landau-Ginzburg scalar field model.

Self-similarity plays a key role in the behavior of fluctuations and interactions.

Abstract

The Casimir interaction energy for a class of discrete self-similar configuration of parallel plates is evaluated using existing methods. The similarities to characteristics of an attractive Casimir force is deduced only at infinite range of configuration. Further, the emergence of Casimir-like energy is qualitatively described for a Gaussian model of Landau-Ginzburg scalar field. Its relevance to self-similarity in the statistical field is shown at infinite range of fluctuations.