Mathematics – Differential Geometry
Scientific paper
2004-06-21
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.
Guilfoyle Brendan
Klingenberg Wilhelm
Sen Siddhartha
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