# Casimir Energies: Temperature Dependence, Dispersion, and Anomalies - Quantum Physics

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Abstract: Assuming the conventional Casimir setting with two thick parallel perfectlyconducting plates of large extent with a homogeneous and isotropic mediumbetween them, we discuss the physical meaning of the electromagnetic fieldenergy $W { m disp}$ when the intervening medium is weakly dispersive butnondissipative. The presence of dispersion means that the energy densitycontains terms of the form $d\omega\epsilon\omega -d\omega$ and$d\omega\mu\omega -d\omega$. We find that, as $W { m disp}$ refersthermodynamically to a non-closed physical system, it is {\it not} to beidentified with the internal thermodynamic energy $U$ following from the freeenergy $F$, or the electromagnetic energy $W$, when the last-mentionedquantities are calculated without such dispersive derivatives. To arrive atthis conclusion, we adopt a model in which the system is a capacitor, linked toan external self-inductance $L$ such that stationary oscillations becomepossible. Therewith the model system becomes a non-closed one. As anintroductory step, we review the meaning of the nondispersive energies, $F, U,$and $W$. As a final topic, we consider an anomaly connected with local surfacedivergences encountered in Casimir energy calculations for higher spacetimedimensions, $D>4$, and discuss briefly its dispersive generalization. This kindof application is essentially a generalization of the treatment of Alnes {\itet al.} J. Phys. A: Math. Theor. {\bf 40}, F315 2007 to the case of amedium-filled cavity between two hyperplanes.

Author: I. Brevik, K. A. Milton

Source: https://arxiv.org/