7 research outputs found
Cancellation of nonrenormalizable hypersurface divergences and the d-dimensional Casimir piston
Using a multidimensional cut-off technique, we obtain expressions for the
cut-off dependent part of the vacuum energy for parallelepiped geometries in
any spatial dimension d. The cut-off part yields nonrenormalizable hypersurface
divergences and we show explicitly that they cancel in the Casimir piston
scenario in all dimensions. We obtain two different expressions for the
d-dimensional Casimir force on the piston where one expression is more
convenient to use when the plate separation a is large and the other when a is
small (a useful duality). The Casimir force on the piston is found
to be attractive (negative) for any dimension d. We apply the d-dimensional
formulas (both expressions) to the two and three-dimensional Casimir piston
with Neumann boundary conditions. The 3D Neumann results are in numerical
agreement with those recently derived in arXiv:0705.0139 using an optical path
technique providing an independent confirmation of our multidimensional
approach. We limit our study to massless scalar fields.Comment: 29 pages; 3 figures; references added; to appear in JHE
Spectral action for torsion with and without boundaries
We derive a commutative spectral triple and study the spectral action for a
rather general geometric setting which includes the (skew-symmetric) torsion
and the chiral bag conditions on the boundary. The spectral action splits into
bulk and boundary parts. In the bulk, we clarify certain issues of the previous
calculations, show that many terms in fact cancel out, and demonstrate that
this cancellation is a result of the chiral symmetry of spectral action. On the
boundary, we calculate several leading terms in the expansion of spectral
action in four dimensions for vanishing chiral parameter of the
boundary conditions, and show that is a critical point of the action
in any dimension and at all orders of the expansion.Comment: 16 pages, references adde
Heat-kernels and functional determinants on the generalized cone
We consider zeta functions and heat-kernel expansions on the bounded,
generalized cone in arbitrary dimensions using an improved calculational
technique. The specific case of a global monopole is analysed in detail and
some restrictions thereby placed on the coefficient. The computation
of functional determinants is also addressed. General formulas are given and
known results are incidentally, and rapidly, reproduced.Comment: 26p,LaTeX.(Cosmetic changes and eqns (9.8),(11.2) corrected.
Electromagnetic Casimir densities for a wedge with a coaxial cylindrical shell
Vacuum expectation values of the field square and the energy-momentum tensor
for the electromagnetic field are investigated for the geometry of a wedge with
a coaxal cylindrical boundary. All boundaries are assumed to be perfectly
conducting and both regions inside and outside the shell are considered. By
using the generalized Abel-Plana formula, the vacuum expectation values are
presented in the form of the sum of two terms. The first one corresponds to the
geometry of the wedge without the cylindrical shell and the second term is
induced by the presence of the shell. The vacuum energy density induced by the
shell is negative for the interior region and is positive for the exterior
region. The asymptotic behavior of the vacuum expectation values are
investigated in various limiting cases. It is shown that the vacuum forces
acting on the wedge sides due to the presence of the cylindrical boundary are
always attractive.Comment: 21 pages, 7 figure
Finite temperature Casimir effect in piston geometry and its classical limit
We consider the Casimir force acting on a -dimensional rectangular piston
due to massless scalar field with periodic, Dirichlet and Neumann boundary
conditions and electromagnetic field with perfect electric conductor and
perfect magnetic conductor boundary conditions. It is verified analytically
that at any temperature, the Casimir force acting on the piston is always an
attractive force pulling the piston towards the interior region, and the
magnitude of the force gets larger as the separation gets smaller. Explicit
exact expressions for the Casimir force for small and large plate separations
and for low and high temperatures are computed. The limits of the Casimir force
acting on the piston when some pairs of transversal plates are large are also
derived. An interesting result regarding the influence of temperature is that
in contrast to the conventional result that the leading term of the Casimir
force acting on a wall of a rectangular cavity at high temperature is the
Stefan--Boltzmann (or black body radiation) term which is of order ,
it is found that the contributions of this term from the interior and exterior
regions cancel with each other in the case of piston. The high temperature
leading order term of the Casimir force acting on the piston is of order ,
which shows that the Casimir force has a nontrivial classical
limit
Thermal Casimir effect in ideal metal rectangular boxes
The thermal Casimir effect in ideal metal rectangular boxes is considered
using the method of zeta functional regularization. The renormalization
procedure is suggested which provides the finite expression for the Casimir
free energy in any restricted quantization volume. This expression satisfies
the classical limit at high temperature and leads to zero thermal Casimir force
for systems with infinite characteristic dimensions. In the case of two
parallel ideal metal planes the results, as derived previously using thermal
quantum field theory in Matsubara formulation and other methods, are reproduced
starting from the obtained expression. It is shown that for rectangular boxes
the temperature-dependent contribution to the electromagnetic Casimir force can
be both positive and negative depending on side lengths. The numerical
computations of the scalar and electromagnetic Casimir free energy and force
are performed for cubesComment: 10 pages, 4 figures, to appear in Europ. Phys. J.