Partition function for a singular background

We present a method for evaluating the partition function in a varying external field. Specifically, we look at the case of a non-interacting, charged, massive scalar field at finite temperature with an associated chemical potential in the background of a delta-function potential. Whilst we present a general method, valid at all temperatures, we only give the result for the leading order term in the high temperature limit. Although the derivative expansion breaks down for inhomogeneous backgrounds we are able to obtain the high temperature expansion, as well as an analytic expression for the zero point energy, by way of a different approximation scheme, which we call the {\it local Born approximation} (LBA).Comment: 5 pages, 1 figure, revtex4, typos corrected. To appear in Phys. Lett.

On the Zero-Point Energy of a Conducting Spherical Shell

The zero-point energy of a conducting spherical shell is evaluated by imposing boundary conditions on the potential, and on the ghost fields. The scheme requires that temporal and tangential components of perturbations of the potential should vanish at the boundary, jointly with the gauge-averaging functional, first chosen of the Lorenz type. Gauge invariance of such boundary conditions is then obtained provided that the ghost fields vanish at the boundary. Normal and longitudinal modes of the potential obey an entangled system of eigenvalue equations, whose solution is a linear combination of Bessel functions under the above assumptions, and with the help of the Feynman choice for a dimensionless gauge parameter. Interestingly, ghost modes cancel exactly the contribution to the Casimir energy resulting from transverse and temporal modes of the potential, jointly with the decoupled normal mode of the potential. Moreover, normal and longitudinal components of the potential for the interior and the exterior problem give a result in complete agreement with the one first found by Boyer, who studied instead boundary conditions involving TE and TM modes of the electromagnetic field. The coupled eigenvalue equations for perturbative modes of the potential are also analyzed in the axial gauge, and for arbitrary values of the gauge parameter. The set of modes which contribute to the Casimir energy is then drastically changed, and comparison with the case of a flat boundary sheds some light on the key features of the Casimir energy in non-covariant gauges.Comment: 29 pages, Revtex, revised version. In this last version, a new section has been added, devoted to the zero-point energy of a conducting spherical shell in the axial gauge. A second appendix has also been include

Neutrino Dark Energy and Moduli Stabilization in a BPS Braneworld Scenario

A braneworld model for neutrino Dark Energy (DE) is presented. We consider a five dimensional two-branes set up with a bulk scalar field motivated by supergravity. Its low-energy effective theory is derived with a moduli space approximation (MSA). The position of the two branes are parametrized by two scalar degrees of freedom (moduli). After detuning the brane tensions a classical potential for the moduli is generated. This potential is unstable for dS branes and we suggest to consider as a stabilizing contribution the Casimir energy of bulk fields. In particular we add a massive spinor (neutrino) field in the bulk and then evaluate the Casimir contribution of the bulk neutrino with the help of zeta function regularization techniques. We construct an explicit form of the 4D neutrino mass as function of the two moduli. To recover the correct DE scale for the moduli potential the usual cosmological constant fine-tuning is necessary, but, once accepted, this model suggests a stronger connection between DE and neutrino physics.Comment: 26 pages, 1 EPS figur

Casimir effect for scalar fields under Robin boundary conditions on plates

We study the Casimir effect for scalar fields with general curvature coupling subject to mixed boundary conditions $(1+\beta_{m}n^{\mu}\partial_{\mu})\phi =0$ at $x=a_{m}$ on one ($m=1$) and two ($m=1,2$) parallel plates at a distance $a\equiv a_{2}-a_{1}$ from each other. Making use of the generalized Abel-Plana formula previously established by one of the authors \cite{Sahrev}, the Casimir energy densities are obtained as functions of $\beta_{1}$ and of $\beta_{1}$,$\beta_{2}$,$a$, respectively. In the case of two parallel plates, a decomposition of the total Casimir energy into volumic and superficial contributions is provided. The possibility of finding a vanishing energy for particular parameter choices is shown, and the existence of a minimum to the surface part is also observed. We show that there is a region in the space of parameters defining the boundary conditions in which the Casimir forces are repulsive for small distances and attractive for large distances. This yields to an interesting possibility for stabilizing the distance between the plates by using the vacuum forces.Comment: 21 pages, 8 figures, consideration of the contribution from complex eigenmodes added, possibility for the stabilization of the distance between the plates is discussed; accepted for publication in J. Phys.

Sonoluminescence as a QED vacuum effect. I: The Physical Scenario

Several years ago Schwinger proposed a physical mechanism for sonoluminescence in terms of changes in the properties of the quantum-electrodynamic (QED) vacuum state. This mechanism is most often phrased in terms of changes in the Casimir Energy: changes in the distribution of zero-point energies and has recently been the subject of considerable controversy. The present paper further develops this quantum-vacuum approach to sonoluminescence: We calculate Bogolubov coefficients relating the QED vacuum states in the presence of a homogeneous medium of changing dielectric constant. In this way we derive an estimate for the spectrum, number of photons, and total energy emitted. We emphasize the importance of rapid spatio-temporal changes in refractive indices, and the delicate sensitivity of the emitted radiation to the precise dependence of the refractive index as a function of wavenumber, pressure, temperature, and noble gas admixture. Although the physics of the dynamical Casimir effect is a universal phenomenon of QED, specific experimental features are encoded in the condensed matter physics controlling the details of the refractive index. This calculation places rather tight constraints on the possibility of using the dynamical Casimir effect as an explanation for sonoluminescence, and we are hopeful that this scenario will soon be amenable to direct experimental probes. In a companion paper we discuss the technical complications due to finite-size effects, but for reasons of clarity in this paper we confine attention to bulk effects.Comment: 25 pages, LaTeX 209, ReV-TeX 3.2, eight figures. Minor revisions: Typos fixed, references updated, minor changes in numerical estimates, minor changes in some figure

Vacuum Energy and Renormalization on the Edge

The vacuum dependence on boundary conditions in quantum field theories is analysed from a very general viewpoint. From this perspective the renormalization prescriptions not only imply the renormalization of the couplings of the theory in the bulk but also the appearance of a flow in the space of boundary conditions. For regular boundaries this flow has a large variety of fixed points and no cyclic orbit. The family of fixed points includes Neumann and Dirichlet boundary conditions. In one-dimensional field theories pseudoperiodic and quasiperiodic boundary conditions are also RG fixed points. Under these conditions massless bosonic free field theories are conformally invariant. Among all fixed points only Neumann boundary conditions are infrared stable fixed points. All other conformal invariant boundary conditions become unstable under some relevant perturbations. In finite volumes we analyse the dependence of the vacuum energy along the trajectories of the renormalization group flow providing an interesting framework for dark energy evolution. On the contrary, the renormalization group flow on the boundary does not affect the leading behaviour of the entanglement entropy of the vacuum in one-dimensional conformally invariant bosonic theories.Comment: 10 pages, 1 eps figur

Wightman function and Casimir densities on AdS bulk with application to the Randall-Sundrum braneworld

Positive frequency Wightman function and vacuum expectation value of the energy-momentum tensor are computed for a massive scalar field with general curvature coupling parameter subject to Robin boundary conditions on two parallel plates located on $D+1$ - dimensional AdS background. The general case of different Robin coefficients on separate plates is considered. The mode summation method is used with a combination of a variant of the generalized Abel-Plana formula for the series over zeros of combinations of cylinder functions. This allows us to extract manifestly the parts due to the AdS spacetime without boundaries and boundary induced parts. The asymptotic behavior of the vacuum densities near the plates and at large distances is investigated. The vacuum forces acting on the boundaries are presented as a sum of the self-action and interaction forces. The first one contains well-known surface divergences and needs further regularization. The interaction forces between the plates are attractive for Dirichlet scalar. We show that threre is a region in the space of parameters defining the boundary conditions in which the interaction forces are repulsive for small distances and attractive for large distances. An application to the Randall-Sundrum braneworld with arbitrary mass terms on the branes is discussed.Comment: 26 pages, 6 figures, discussions and figure labels added, accepted for publication in Nuclear Physics

Scalar Casimir densities for cylindrically symmetric Robin boundaries

Wightman function, the vacuum expectation values of the field square and the energy-momentum tensor are investigated for a massive scalar field with general curvature coupling parameter in the region between two coaxial cylindrical boundaries. It is assumed that the field obeys general Robin boundary conditions on bounding surfaces. The application of a variant of the generalized Abel-Plana formula allows to extract from the expectation values the contribution from single shells and to present the interference part in terms of exponentially convergent integrals. The vacuum forces acting on the boundaries are presented as the sum of self-action and interaction terms. The first one contains well-known surface divergences and needs a further renormalization. The interaction forces between the cylindrical boundaries are finite and are attractive for special cases of Dirichlet and Neumann scalars. For the general Robin case the interaction forces can be both attractive or repulsive depending on the coefficients in the boundary conditions. The total Casimir energy is evaluated by using the zeta function regularization technique. It is shown that it contains a part which is located on bounding surfaces. The formula for the interference part of the surface energy is derived and the energy balance is discussed.Comment: 22 pages, 5 figure

Spectral asymptotics of Euclidean quantum gravity with diff-invariant boundary conditions

A general method is known to exist for studying Abelian and non-Abelian gauge theories, as well as Euclidean quantum gravity, at one-loop level on manifolds with boundary. In the latter case, boundary conditions on metric perturbations h can be chosen to be completely invariant under infinitesimal diffeomorphisms, to preserve the invariance group of the theory and BRST symmetry. In the de Donder gauge, however, the resulting boundary-value problem for the Laplace type operator acting on h is known to be self-adjoint but not strongly elliptic. The latter is a technical condition ensuring that a unique smooth solution of the boundary-value problem exists, which implies, in turn, that the global heat-kernel asymptotics yielding one-loop divergences and one-loop effective action actually exists. The present paper shows that, on the Euclidean four-ball, only the scalar part of perturbative modes for quantum gravity are affected by the lack of strong ellipticity. Further evidence for lack of strong ellipticity, from an analytic point of view, is therefore obtained. Interestingly, three sectors of the scalar-perturbation problem remain elliptic, while lack of strong ellipticity is confined to the remaining fourth sector. The integral representation of the resulting zeta-function asymptotics is also obtained; this remains regular at the origin by virtue of a spectral identity here obtained for the first time.Comment: 25 pages, Revtex-4. Misprints in Eqs. (5.11), (5.14), (5.16) have been correcte