On the Vacuum energy of a Color Magnetic Vortex

We calculate the one loop gluon vacuum energy in the background of a color magnetic vortex for SU(2) and SU(3). We use zeta functional regularization to obtain analytic expressions suitable for numerical treatment. The momentum integration is turned to the imaginary axis and fast converging sums/integrals are obtained. We investigate numerically a number of profiles of the background. In each case the vacuum energy turns out to be positive increasing in this way the complete energy and making the vortex configuration less stable. In this problem bound states (tachyonic modes) are present for all investigated profiles making them intrinsically unstable.Comment: 28 pages, 4 figure

Generalized Lifshitz formula for a cylindrical plasma sheet in front of a plane beyond proximity force approximation

We calculate the first correction beyond proximity force approximation for a cylindrical graphene sheet in interaction with a flat graphene sheet or a dielectric half space.Comment: 35 pages, 8 figure

Heat kernel Coefficients and Divergencies of the Casimir Energy for the Dispersive Sphere

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.Comment: 8 pages, Contribution to the 5th Workshop on Quantum Field Theory under the Influence of External Conditions, Leipzig, Germany, 10-14 Sep 200

Casimir and Casimir-Polder forces with dissipation from first principles

We consider Casimir-Polder and Casimir forces with finite dissipation by coupling heat baths to the dipoles introducing, this way, dissipation from 'first principles'. We derive a representation of the free energy as an integral over real frequencies, which can be viewd as an generalization of the 'remarkable formula' introduced by Ford et. al. 1985. For instance, we obtain a nonperturbative representation for the atom-atom and atom-wall interactions. We investigate several limiting cases. From the limit $T\to0$ we show that the third law of thermodynamics cannot be violated within the given approach, where the dissipation parameter cannot depend on temperature 'by construction'. We conclude, that the given approach is insufficient to resolve the thermodynamic puzzle connected with the Drude model when inserted into the Lifshitz formula. Further we consider the transition to Matsubara representation and discuss modifications of the contribution from the zeroth Matsubara frequency.Comment: 20 pages, several misprints correcte

Vacuum energy in the presence of a magnetic string with delta function profile

We present a calculation of the ground state energy of massive spinor fields and massive scalar fields in the background of an inhomogeneous magnetic string with potential given by a delta function. The zeta functional regularization is used and the lowest heat kernel coefficients are calculated. The rest of the analytical calculation adopts the Jost function formalism. In the numerical part of the work the renormalized vacuum energy as a function of the radius $R$ of the string is calculated and plotted for various values of the strength of the potential. The sign of the energy is found to change with the radius. For both scalar and spinor fields the renormalized energy shows no logarithmic behaviour in the limit $R\to 0$, as was expected from the vanishing of the heat kernel coefficient $A_2$, which is not zero for other types of profiles.Comment: 30 pages, 10 figure

The heat kernel coefficients for the dielectric cylinder

We calculate the \hkks for the \elm field in the background of a dielectric cylinder with non equal speeds of light inside and outside. The coefficient $a_{2}$ whose vanishing makes the vacuum energy of a massless field unique, turns out to be zero in dilute order, i.e., in order (\ep-1)^{2}, and nonzero beyond. As a consequence, the vanishing of the vacuum energy in the presence of a dielectric cylinder found by Casimir-Polder summation must take place irrespectively of the methods by which it might be calculated.Comment: 14 pages, 1 figur

The Casimir effect for thin plasma sheets and the role of the surface plasmons

We consider the Casimir force betweeen two dielectric bodies described by the plasma model and between two infinitely thin plasma sheets. In both cases in addition to the photon modes surface plasmons are present in the spectrum of the electromagnetic field. We investigate the contribution of both types of modes to the Casimir force and confirm resp. find in both models large compensations between the plasmon modes themselves and between them and the photon modes especially at large distances. Our conclusion is that the separation of the vacuum energy into plasmon and photon contributions must be handled with care except for the case of small separations.Comment: submitted to JPhysA Special Issue QFEXT'05, replaced due to a wrong Latex comman

Reconsidering the quantization of electrodynamics with boundary conditions and some measurable consequences

We show that the commonly known conductor boundary conditions $E_{||}=B_\perp=0$ can be realized in two ways which we call 'thick' and 'thin' conductor. The 'thick' conductor is the commonly known approach and includes a Neumann condition on the normal component $E_\perp$ of the electric field whereas for a 'thin' conductor $E_\perp$ remains without boundary condition. Both types describe different physics already on the classical level where a 'thin' conductor allows for an interaction between the normal components of currents on both sides. On quantum level different forces between a conductor and a single electron or a neutral atom result. For instance, the Casimir-Polder force for a 'thin' conductor is by about 13% smaller than for a 'thick' one.Comment: 22 pages, basic statement weakened, conclusions changed, misprints correcte