Title

The Casimir Effect between Non-Parallel Plates by Geometric Optics

Authors

Brendan Guilfoyle, School of Science, Technology, Engineering and Mathematics, Institute of Technology, Tralee, Clash, Tralee, Co. Kerry, Ireland.Follow
Wilhelm Klingenberg, Department of Mathematical Sciences, University of Durham, Durham DH1 3LE, United Kingdom
Siddhartha Sen, School of Mathematics, University of Dublin, Dublin 2, Ireland; Department of Theoretical Physics, IACS, Kolkata, India

ORCID

0000-0002-7437-5046

Document Type

Article

Disciplines

Mathematics | Physical Sciences and Mathematics

Publication Details

Electronic version of an article published as Reviews in Mathematical Physics, vol. 17, no. 8, 2005, 859-880. 10.1142/S0129055X05002431 © World Scientific Publishing Company https://www.worldscientific.com/doi/10.1142/S0129055X05002431

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.

Recommended Citation

The Casimir Effect between non-parallel plates by geometric optics, Brendan Guilfoyle, Wilhelm Klingenberg, Siddhartha Sen (&), Reviews in Mathematical Physics 2005 17:08, 859-880