The Casimir Effect Between Non-Parallel Plates by Geometric Optics

Details The Casimir Effect Between Non-Parallel Plates by Geometric Optics The Casimir Effect Between Non-Parallel Plates by Geometric Optics

2004-06-21

arxiv.org/abs/math/0406399v3

Rev.Math.Phys. 17 (2005) 859-880

Mathematics

Differential Geometry

25 pages, 8 figures, AMS-LATEX

Scientific paper

10.1142/S0129055X05002431

Recent work by Jaffe and Scardicchio has expressed the optical approximation to the Casimir effect as a sum over geometric quantities. The first two authors have developed a technique which uses the complex geometry of the space of oriented affine lines in ${\Bbb{R}}^3$ to describe reflection of rays off a surface. This allows the quantities in the optical approximation to the Casimir effect to be calculated. 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 regularise 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.

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