The Casimir effect between non-parallel plates by geometric optics

Guilfoyle, B.; Klingenberg, W.; Sen, S.

Abstract

The first two authors have developed a technique which uses the complex geometry of the space of oriented affine lines in ℝ3 to describe the reflection of rays off a surface. This can be viewed as a parametric approach to geometric optics which has many possible applications. Recently, Jaffe and Scardicchio have developed a geometric optics approximation to the Casimir effect and the main purpose of this paper is to show that the quantities involved can be easily computed by this complex formalism. To illustrate this, we determine explicitly and in closed form the geometric optics approximation of the Casimir force between two non-parallel plates. By making one of the plates finite, we regularize the divergence that is caused by the intersection of the planes. In the parallel plate limit, we prove that our expression reduces to Casimir's original result.

Citation

Guilfoyle, B., Klingenberg, W., & Sen, S. (2005). The Casimir effect between non-parallel plates by geometric optics. Reviews in Mathematical Physics, 17(8), 859 - 880. https://doi.org/10.1142/s0129055x05002431

• Journal Article Type: Article
• Publication Date: Sep 1, 2005
• Deposit Date: Feb 15, 2008
• Journal: Reviews in Mathematical Physics
• Print ISSN: 0129-055X
• Electronic ISSN: 1793-6659
• Publisher: World Scientific Publishing
• Peer Reviewed: Peer Reviewed
• Volume: 17
• Issue: 8
• Pages: 859 - 880
• DOI: https://doi.org/10.1142/s0129055x05002431
• Keywords: Casimir force, Geometric optics.
• Public URL: https://durham-repository.worktribe.com/output/1594743