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The Casimir effect between non-parallel plates by geometric optics

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


B. Guilfoyle

S. Sen


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.


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.

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
Keywords Casimir force, Geometric optics.