Electromagnetic semitransparent δ\delta-function plate: Casimir interaction energy between parallel infinitesimally thin plates

We derive boundary conditions for electromagnetic fields on a $\delta$-function plate. The optical properties of such a plate are shown to necessarily be anisotropic in that they only depend on the transverse properties of the plate. We unambiguously obtain the boundary conditions for a perfectly conducting $\delta$-function plate in the limit of infinite dielectric response. We show that a material does not "optically vanish" in the thin-plate limit. The thin-plate limit of a plasma slab of thickness $d$ with plasma frequency $\omega_p^2=\zeta_p/d$ reduces to a $\delta$-function plate for frequencies ($\omega=i\zeta$) satisfying $\zeta d \ll \sqrt{\zeta_p d} \ll 1$. We show that the Casimir interaction energy between two parallel perfectly conducting $\delta$-function plates is the same as that for parallel perfectly conducting slabs. Similarly, we show that the interaction energy between an atom and a perfect electrically conducting $\delta$-function plate is the usual Casimir-Polder energy, which is verified by considering the thin-plate limit of dielectric slabs. The "thick" and "thin" boundary conditions considered by Bordag are found to be identical in the sense that they lead to the same electromagnetic fields.Comment: 21 pages, 7 figures, references adde

Assay validity of point-of-care platelet function tests in thrombocytopenic blood samples

Point-of-care (POC) platelet function tests are faster and easier to perform than in-depth assessment by flow cytometry. At low platelet counts, however, POC tests are prone to assess platelet function incorrectly. Lower limits of platelet count required to obtain valid test results were defined and a testing method to facilitate comparability between different tests was established. We assessed platelet function in whole blood samples of healthy volunteers at decreasing platelet counts (> 100, 80-100, 50-80, 30-50 and < 30 x109/L) using two POC tests: impedance aggregometry and in-vitro bleeding time. Flow cytometry served as the gold standard. The number of platelets needed to reach 50% of the maximum function (ED50) and the lower reference limit (EDref) were calculated to define limits of test validity. The minimal platelet count required for reliable test results was 100 x109/L for impedance aggregometry and in-vitro bleeding time but only 30 x109/L for flow cytometry. Comparison of ED50 and EDref showed significantly lower values for flow cytometry than either POC test (P value < 0.05) but no difference between POC tests nor between the used platelet agonists within a test method. Calculating the ED50 and EDref provides an effective way to compare values from different platelet function assays. Flow cytometry enables correct platelet function testing as long as platelet count is > 30 x109/L whereas impedance aggregometry and in-vitro bleeding time are inconsistent unless platelet count is > 100 x109/L

Semiclassical Casimir Energies at Finite Temperature

We study the dependence on the temperature T of Casimir effects for a range of systems, and in particular for a pair of ideal parallel conducting plates, separated by a vacuum. We study the Helmholtz free energy, combining Matsubara's formalism, in which the temperature appears as a periodic Euclidean fourth dimension of circumference 1/T, with the semiclassical periodic orbital approximation of Gutzwiller. By inspecting the known results for the Casimir energy at T=0 for a rectangular parallelepiped, one is led to guess at the expression for the free energy of two ideal parallel conductors without performing any calculation. The result is a new form for the free energy in terms of the lengths of periodic classical paths on a two-dimensional cylinder section. This expression for the free energy is equivalent to others that have been obtained in the literature. Slightly extending the domain of applicability of Gutzwiller's semiclassical periodic orbit approach, we evaluate the free energy at T>0 in terms of periodic classical paths in a four-dimensional cavity that is the tensor product of the original cavity and a circle. The validity of this approach is at present restricted to particular systems. We also discuss the origin of the classical form of the free energy at high temperatures.Comment: 17 pages, no figures, Late

Nonperturbative Gauge Fixing and Perturbation Theory

We compare the gauge-fixing approach proposed by Jona-Lasinio and Parrinello, and by Zwanziger (JPLZ) with the standard Fadeev-Popov procedure, and demonstrate perturbative equality of gauge-invariant quantities, up to irrelevant terms induced by the cutoff. We also show how a set of local, renormalizable Feynman rules can be constructed for the JPLZ procedure.Comment: 9 pages, latex, version to appear in Phys. Rev.

The heavy quark decomposition of the S-matrix and its relation to the pinch technique

We propose a decomposition of the S-matrix into individually gauge invariant sub-amplitudes, which are kinematically akin to propagators, vertices, boxes, etc. This decompsition is obtained by considering limits of the S-matrix when some or all of the external particles have masses larger than any other physical scale. We show at the one-loop level that the effective gluon self-energy so defined is physically equivalent to the corresponding gauge independent self-energy obtained in the framework of the pinch technique. The generalization of this procedure to arbitrary gluonic $n$-point functions is briefly discussed.Comment: 11 uuencoded pages, NYU-TH-94/10/0

Semiclassical Estimates of Electromagnetic Casimir Self-Energies of Spherical and Cylindrical Metallic Shells

The leading semiclassical estimates of the electromagnetic Casimir stresses on a spherical and a cylindrical metallic shell are within 1% of the field theoretical values. The electromagnetic Casimir energy for both geometries is given by two decoupled massless scalars that satisfy conformally covariant boundary conditions. Surface contributions vanish for smooth metallic boundaries and the finite electromagnetic Casimir energy in leading semiclassical approximation is due to quadratic fluctuations about periodic rays in the interior of the cavity only. Semiclassically the non-vanishing Casimir energy of a metallic cylindrical shell is almost entirely due to Fresnel diffraction.Comment: 12 pages, 2 figure

Comments on the Sign and Other Aspects of Semiclassical Casimir Energies

The Casimir energy of a massless scalar field is semiclassically given by contributions due to classical periodic rays. The required subtractions in the spectral density are determined explicitly. The so defined semiclassical Casimir energy coincides with that obtained using zeta function regularization in the cases studied. Poles in the analytic continuation of zeta function regularization are related to non-universal subtractions in the spectral density. The sign of the Casimir energy of a scalar field on a smooth manifold is estimated by the sign of the contribution due to the shortest periodic rays only. Demanding continuity of the Casimir energy under small deformations of the manifold, the method is extended to integrable systems. The Casimir energy of a massless scalar field on a manifold with boundaries includes contributions due to periodic rays that lie entirely within the boundaries. These contributions in general depend on the boundary conditions. Although the Casimir energy due to a massless scalar field may be sensitive to the physical dimensions of manifolds with boundary, its sign can in favorable cases be inferred without explicit calculation of the Casimir energy.Comment: 39 pages, no figures, references added, some correction

On ghost condensation, mass generation and Abelian dominance in the Maximal Abelian Gauge

Recent work claimed that the off-diagonal gluons (and ghosts) in pure Yang-Mills theories, with Maximal Abelian gauge fixing (MAG), attain a dynamical mass through an off-diagonal ghost condensate. This condensation takes place due to a quartic ghost interaction, unavoidably present in MAG for renormalizability purposes. The off-diagonal mass can be seen as evidence for Abelian dominance. We discuss why ghost condensation of the type discussed in those works cannot be the reason for the off-diagonal mass and Abelian dominance, since it results in a tachyonic mass. We also point out what the full mechanism behind the generation of a real mass might look like.Comment: 7 pages; uses revtex

Of Some Theoretical Significance: Implications of Casimir Effects

In his autobiography Casimir barely mentioned the Casimir effect, but remarked that it is "of some theortical significance." We will describe some aspects of Casimir effects that appear to be of particular significance now, more than half a century after Casimir's famous paper

Equivariant Gauge Fixing of SU(2) Lattice Gauge Theory

I construct a Lattice Gauge Theory (LGT) with discrete Z_2 structure group and an equivariant BRST symmetry that is physically equivalent to the standard SU(2)-LGT. The measure of this Z_2-LGT is invariant under all the discrete symmetries of the lattice and its partition function does not vanish. The Topological Lattice Theories (TLT) that localize on the moduli spaces are explicitly constructed and their BRST symmetry is exhibited. The ghosts of the Z_2-invariant local LGT are integrated in favor of a nonlocal bosonic measure. In addition to the SU(2) link variables and the coupling g^2, this effective bosonic measure also depends on an auxiliary gauge invariant site variable of canonical dimension two and on a gauge parameter \alpha. The relation between the expectation value of the auxiliary field, the gauge parameter \alpha and the lattice spacing $a$ is obtained to lowest order in the loop expansion. In four dimensions and the critical limit this expectation value is a physical scale proportional to \Lambda_L in the gauge \alpha=g^2 (11-n_f)/24+ O(g^4). Implications for the loop expansion of observables in such a critical gauge are discussed.Comment: 46 pages, Latex, updated and shortened version to appear in Phys.Rev.