A mathematical analysis of Casimir interactions I: The scalar field
Yan-Long Fang, Alexander Strohmaier
TL;DR
This paper rigorously compares three mathematical methods for calculating Casimir forces in scalar quantum fields, establishing their equivalence through precise proofs.
Contribution
It provides a rigorous mathematical framework for three approaches to Casimir force computation and proves their equivalence.
Findings
Three methods for Casimir force calculation are mathematically equivalent.
Rigorous formulations of Casimir interactions for scalar fields are established.
The paper clarifies the mathematical foundations of Casimir effect computations.
Abstract
Starting from the construction of the free quantum scalar field of mass we give mathematically precise and rigorous versions of three different approaches to computing the Casimir forces between compact obstacles. We then prove that they are equivalent.
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