The heat-kernel coefficient a[sub 2] and the Casimir energy of a dielectric cylinder

2001 ◽  
Author(s):  
M. Bordag
Keyword(s):  
Heat Kernel ◽  
Casimir Energy ◽  
Dielectric Cylinder

scholarly journals Heat kernel coefficients for the dielectric cylinder

2001 ◽  
Vol 64 (2) ◽  
Author(s):  
M. Bordag ◽  
I. G. Pirozhenko
Keyword(s):  
Heat Kernel ◽  
Dielectric Cylinder

scholarly journals CASIMIR ENERGY OF 5D ELECTRO-MAGNETISM AND SPHERE LATTICE REGULARIZATION

2008 ◽  
Vol 23 (14n15) ◽  
pp. 2245-2248 ◽  
Author(s):  
SHOICHI ICHINOSE
Keyword(s):  
Renormalization Group ◽  
Closed Form ◽  
Heat Kernel ◽  
Kernel Method ◽  
Casimir Energy ◽  
Closed String ◽  
Extra Space ◽  
Lattice Regularization ◽  
Expanded Form ◽  
Perturbative Treatment

Casimir energy is calculated in the 5D warped system. It is compared with the flat one. The position/ momentum propagator is exploited. A new regularization, called sphere lattice regularization, is introduced. It is a direct realization of the geometrical interpretation of the renormalization group. The regularized configuration is closed-string like. We do not take the KK-expansion approach. Instead the P/M propagator is exploited, combined with the heat-kernel method. All expressions are closed-form (not KK-expanded form). Rigorous quantities are only treated (non-perturbative treatment). The properly regularized form of Casimir energy, is expressed in the closed form. We numerically evaluate its Λ(4D UV-cutoff), ω(5D bulk curvature, warpedness parameter) and T(extra space IR parameter) dependence.

scholarly journals HEAT KERNEL COEFFICIENTS AND DIVERGENCIES OF THE CASIMIR ENERGY FOR THE DISPERSIVE SPHERE

2002 ◽  
Vol 17 (06n07) ◽  
pp. 813-819 ◽  
Author(s):  
M. BORDAG ◽  
K. KIRSTEN
Keyword(s):  
Electromagnetic Field ◽  
Heat Kernel ◽  
Ground State Energy ◽  
Ground State ◽  
High Frequency ◽  
Vacuum Energy ◽  
State Energy ◽  
Casimir Energy ◽  
Divergent Part

The first heat kernel coefficients are calculated for a dispersive ball whose permittivity at high frequency differs from unity by inverse powers of the frequency. The corresponding divergent part of the vacuum energy of the electromagnetic field is given and ultraviolet divergencies are seen to be present. Also in a model where the number of atoms is fixed the pressure exhibits infinities. As a consequence, the ground-state energy for a dispersive dielectric ball cannot be interpreted easily.

HEAT-KERNEL APPROACH TO THE ZETA-FUNCTION REGULARIZATION OF THE CASIMIR ENERGY FOR DOMAINS WITH CURVED BOUNDARIES

1990 ◽  
Vol 05 (09) ◽  
pp. 1653-1669 ◽  
Author(s):  
E. ELIZALDE ◽  
A. ROMEO
Keyword(s):  
Zeta Function ◽  
Heat Kernel ◽  
Vacuum Energy ◽  
Space Dimension ◽  
Casimir Energy ◽  
Scale Dependence ◽  
Geometrical Object ◽  
Curved Boundaries ◽  
Kernel Approach ◽  
Function Definition

We combine a zeta-function definition and heat-kernel series to derive Casimir energy expansions parametrizing the UV divergences in the presence of arbitrarily shaped smooth boundaries. Their terms, in the form of a geometrical object times a divergence, allow for drawing conclusions on the scale dependence and on the finiteness of the vacuum energy when limiting surfaces have been introduced. Different behaviors are found depending, among other factors, on the even or odd character of the space dimension. A number of controversial points are cleared up and some misstatements in the literature are properly rigorized.

scholarly journals Casimir energy for a dielectric cylinder

2005 ◽  
Vol 320 (1) ◽  
pp. 108-134 ◽  
Author(s):  
Inés Cavero-Peláez ◽  
Kimball A. Milton
Keyword(s):  
Casimir Energy ◽  
Dielectric Cylinder
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