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DESCRIPTION:Genya Kolomeisky\, University of Virginia\n\nThe Casimir self-e
nergy of a boundary is ultraviolet-divergent. In many cases the divergence
s can be eliminated by methods such as zeta- function regularization or th
rough physical arguments (ultraviolet transparency of the boundary would p
rovide a cutoff). Using the example of a massless scalar field theory with
a Dirichlet boundary we explore the relationship between such approaches\
, with the goal of better understanding the origin of the divergences. We
are guided by the insight due to Dowker and Kennedy (1978) and Deutsch and
Candelas (1979)\, that the divergences represent measurable effects that
can be interpreted with the aid of the theory of the asymptotic distributi
on of eigenvalues of the Laplacian first discussed by Weyl. In many cases
the Casimir self-energy is the sum of cutoff-dependent (Weyl) terms having
geometrical origin\, and an "intrinsic" term that is independent of the c
utoff. The Weyl terms make a measurable contribution to the physical situa
tion even when regularization methods succeed in isolating the intrinsic p
art. Regularization methods fail when the Weyl terms and intrinsic parts o
f the Casimir effect cannot be clearly separated. Specifically\, we demons
trate that the Casimir self-energy of a smooth boundary in two dimensions
is a sum of two Weyl terms (exhibiting quadratic and logarithmic cutoff de
pendence)\, a geometrical term that is independent of cutoff\, and a non-g
eometrical intrinsic term. As by-products we resolve the puzzle of the div
ergent Casimir force on a ring and correct the sign of the coefficient of
linear tension of the Dirichlet line predicted in earlier treatments. \n \
n
DTSTART:20100326T200000Z
LOCATION:Physics Building\, Room 204
SUMMARY:Casimir effect due to a single boundary as a manifestation of the W
eyl problem
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