Kirsten, K. (2013) The Casimir effect and its mathematical implications. Il nuovo cimento C, 36 (3). pp. 139-162. ISSN 1826-9885
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Abstract
We describe the Casimir effect in the context of a spectral problem resulting from partial differential equations. Different formulations, namely the local vacuum energy density, Green’s functions and functional determinants are used to give formal expressions for the Casimir energy. Regularizations then employed are the zeta function, the frequency-cutoff and point splitting in combination with Green’s functions. Examples for single-body Casimir energies are considered. Singularities related to ambiguities are associated with heat kernel coefficients, invariants that describe the small-t asymptotics of the heat kernel. Renormalization is discussed in terms of these, in particular the coefficients are used to elegantly discuss if given configurations lead to unambiguous predictions for the Casimir energy and/or force. An example for the singularity-free situation is the Casimir force between separate bodies and a formalism for its computation is given.
| Item Type: | Article |
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| Uncontrolled Keywords: | Theory of quantized fields ; Spectral methods |
| Subjects: | 500 Scienze naturali e Matematica > 530 Fisica |
| Depositing User: | Marina Spanti |
| Date Deposited: | 05 May 2020 12:54 |
| Last Modified: | 05 May 2020 12:54 |
| URI: | http://eprints.bice.rm.cnr.it/id/eprint/18274 |
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