Mode-by-mode summation for the zero point electromagnetic energy of an infinite cylinder

Using the mode-by-mode summation technique the zero point energy of the electromagnetic field is calculated for the boundary conditions given on the surface of an infinite solid cylinder. It is assumed that the dielectric and magnetic characteristics of the material which makes up the cylinder $(\epsilon_1, \mu_1)$ and of that which makes up the surroundings $(\epsilon_2, \mu_2)$ obey the relation $\epsilon_1\mu_1= \epsilon_2\mu_2$. With this assumption all the divergences cancel. The divergences are regulated by making use of zeta function techniques. Numerical calculations are carried out for a dilute dielectric cylinder and for a perfectly conducting cylindrical shell. The Casimir energy in the first case vanishes, and in the second is in complete agreement with that obtained by DeRaad and Milton who employed a Green's function technique with an ultraviolet regulator.Comment: REVTeX, 16 pages, no figures and tables; transcription error in previous version corrected, giving a zero Casimir energy for a tenuous cylinde

The ννγ\nu \nu \gamma Amplitude in an External Homogeneous Electromagnetic Field

Neutrino-photon interactions in the presence of an external homogeneous constant electromagnetic field are studied. The $\nu \nu \gamma$ amplitude is calculated in an electromagnetic field of the general type, when the two field invariants are nonzero.Comment: 7 pages, 1 figur

Vector Casimir effect for a D-dimensional sphere

The Casimir energy or stress due to modes in a D-dimensional volume subject to TM (mixed) boundary conditions on a bounding spherical surface is calculated. Both interior and exterior modes are included. Together with earlier results found for scalar modes (TE modes), this gives the Casimir effect for fluctuating ``electromagnetic'' (vector) fields inside and outside a spherical shell. Known results for three dimensions, first found by Boyer, are reproduced. Qualitatively, the results for TM modes are similar to those for scalar modes: Poles occur in the stress at positive even dimensions, and cusps (logarithmic singularities) occur for integer dimensions $D\le1$. Particular attention is given the interesting case of D=2.Comment: 20 pages, 1 figure, REVTe

Weak reaction freeze-out constraints on primordial magnetic fields

We explore constraints on the strength of the primordial magnetic field based upon the weak reaction freeze-out in the early universe. We find that limits on the strength of the magnetic field found in other works are recovered simply by examining the temperature at which the rate of weak reactions drops below the rate of universal expansion ($\Gamma_{w} \le$ H). The temperature for which the $n/p$ ratio at freeze-out leads to acceptable helium production implies limits on the magnetic field. This simplifies the application of magnetic fields to other cosmological variants of the standard big-bang. As an illustration we also consider effects of neutrino degeneracy on the allowed limits to the primordial magnetic field.Comment: Submitted to Phys. Rev. D., 6 pages, 2 figure

Casimir Energy for Spherical boundaries

Calculations of the Casimir energy for spherical geometries which are based on integrations of the stress tensor are critically examined. It is shown that despite their apparent agreement with numerical results obtained from mode summation methods, they contain a number of serious errors. Specifically, these include (1) an improper application of the stress tensor to spherical boundaries, (2) the neglect of pole terms in contour integrations, and (3) the imposition of inappropriate boundary conditions upon the relevant propagators. A calculation which is based on the stress tensor and which avoids such problems is shown to be possible. It is, however, equivalent to the mode summation method and does not therefore constitute an independent calculation of the Casimir energy.Comment: Revtex, 7 pages, Appendix added providing details of failure of stress tensor metho

Neutrino emission via the plasma process in a magnetized plasma

Neutrino emission via the plasma process using the vertex formalism for QED in a strongly magnetized plasma is considered. A new vertex function is introduced to include the axial vector part of the weak interaction. Our results are compared with previous calculations, and the effect of the axial vector coupling on neutrino emission is discussed. The contribution from the axial vector coupling can be of the same order as or greater than the vector vector coupling under certain plasma conditions.Comment: 20 pages, 3 figure

On the G2G_2 Manifestation for Longitudinally Polarized

The contribution of the $G_2$ structure function to polarized deep inelastic scattering is slightly redefined in order to avoid kinematical zeros. Its strong $Q^2$-dependence implied by the Burkhardt-Cottingham (BC) sum rule naturally explains the sign change of the generalized Gerasimov-Drell-Hearn (GDH) sum rule. The status of the BC sum rule and implications for other spin processes are discussed.Comment: 16 pages,CPT-94/P.3014,late

Casimir effect for a DD-dimensional sphere

The Casimir force on a $D$-dimensional sphere due to the confinement of a massless scalar field is computed as a function of $D$, where $D$ is a continuous variable that ranges from $-\infty$ to $\infty$. The dependence of the force on the dimension is obtained using a simple and straightforward Green's function technique. We find that the Casimir force vanishes as $D\to +\infty$ ($D$ non-even integer) and also vanishes when $D$ is a negative even integer. The force has simple poles at positive even integer values of $D$.Comment: 22 pages, REVTeX, 4 uuencoded figures, OKHEP-94-0

Casimir Energy for a Spherical Cavity in a Dielectric: Applications to Sonoluminescence

In the final few years of his life, Julian Schwinger proposed that the ``dynamical Casimir effect'' might provide the driving force behind the puzzling phenomenon of sonoluminescence. Motivated by that exciting suggestion, we have computed the static Casimir energy of a spherical cavity in an otherwise uniform material. As expected the result is divergent; yet a plausible finite answer is extracted, in the leading uniform asymptotic approximation. This result agrees with that found using zeta-function regularization. Numerically, we find far too small an energy to account for the large burst of photons seen in sonoluminescence. If the divergent result is retained, it is of the wrong sign to drive the effect. Dispersion does not resolve this contradiction. In the static approximation, the Fresnel drag term is zero; on the mother hand, electrostriction could be comparable to the Casimir term. It is argued that this adiabatic approximation to the dynamical Casimir effect should be quite accurate.Comment: 23 pages, no figures, REVTe

High temperature asymptotics of thermodynamic functions of electromagnetic field subjected to boundary conditions on a sphere and cylinder

The high temperature asymptotics of thermodynamic functions of electromagnetic field subjected to boundary conditions with spherical and cylindrical symmetries are constructed by making use of a general expansion in terms of heat kernel coefficients and the related determinant. For this, some new heat kernel coefficients and determinants had to be calculated for the boundary conditions under consideration. The obtained results reproduce all the asymptotics derived by other methods in the problems at hand and involve a few new terms in the high temperature expansions. An obvious merit of this approach is its universality and applicability to any boundary value problem correctly formulated.Comment: 27 pages, REVTeX, no figures, no tables, presentations is improved, a few references are adde