The Mathematics of the Casimir Effect - School of Mathematical ...

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Outline The Casimir Effect Making Sense of Infinity - Infinity Conclusion The Mathematical Setting Divergent Series Euler-Maclaurin Formula Abel-Plana Formula 1 The Casimir Effect 2 Making Sense of Infinity - Infinity The Mathematical Setting Divergent Series Euler-Maclaurin Formula Abel-Plana Formula 3 Conclusion Thomas Prellberg The Mathematics of the Casimir Effect
Spectral Theory The Casimir Effect Making Sense of Infinity - Infinity Conclusion The Mathematical Setting Divergent Series Euler-Maclaurin Formula Abel-Plana Formula Consider −∆ for a compact manifold Ω with a smooth boundary ∂Ω On a suitable function space, this operator is self-adjoint and positive with pure point spectrum One finds formally E discrete = 1 c Trace(−∆)1/2 2 This would be a different talk — let’s keep it simple for today Choose Ω = [0, L] and ∆ = ∂2 ∂x 2 with Dirichlet boundary conditions f (0) = f (L) = 0. Thomas Prellberg The Mathematics of the Casimir Effect
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Zeta Function Regularisation Regula
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