Derivation of Casimir Effect without Zeta-Regularization

TL;DR

This paper offers a new derivation of the Casimir effect that avoids zeta-regularization, providing an alternative perspective on calculating vacuum energy between conducting plates.

Contribution

It introduces a zeta-regularization-free method to derive the Casimir effect, connecting vacuum energy to physical changes and the uncertainty principle.

Findings

Derivation aligns with standard Casimir formula

Provides an alternative to zeta-regularization methods

Enhances understanding of vacuum energy calculations

Abstract

The Casimir effect describes the attractive force arising due to quantum fluctuations of the vacuum electromagnetic field between closely spaced conducting plates. Traditionally, zeta-regularization is employed in calculations to address infinities that emerge during the derivation. This paper presents a novel derivation of the Casimir effect that circumvents the need for zeta-regularization. We derive a formula for the average vacuum energy density between two perfectly conducting plates separated by distance a. Our approach relates the expected vacuum energy to the change in length and position associated with each energy state. The uncertainty principle is incorporated to calculate the area linked to each state. The final result aligns with the standard Casimir effect formula obtained with zeta-regularization. This work demonstrates that the Casimir effect can be derived without relying on zeta-regularization, offering an alternative perspective on this well-established phenomenon.