Thermal Quantum Fields in Static Electromagnetic Backgrounds

We present and discuss, at a general level, new mathematical results on the spatial nonuniformity of thermal quantum fields coupled minimally to static background electromagnetic potentials. Two distinct examples are worked through in some detail: uniform (parallel and perpendicular) background electric and magnetic fields coupled to a thermal quantum scalar field.Comment: 22 page

Casimir piston for massless scalar fields in three dimensions

We study the Casimir piston for massless scalar fields obeying Dirichlet boundary conditions in a three dimensional cavity with sides of arbitrary lengths $a,b$ and $c$ where $a$ is the plate separation. We obtain an exact expression for the Casimir force on the piston valid for any values of the three lengths. As in the electromagnetic case with perfect conductor conditions, we find that the Casimir force is negative (attractive) regardless of the values of $a$, $b$ and $c$. Though cases exist where the interior contributes a positive (repulsive) Casimir force, the total Casimir force on the piston is negative when the exterior contribution is included. We also obtain an alternative expression for the Casimir force that is useful computationally when the plate separation $a$ is large.Comment: 19 pages,3 figures; references updated and typos fixed to match published versio

Chemical potential as a source of stability for gravitating Skyrmions

A discussion of the stability of self gravitating Skyrmions, with a large winding number N, in a Schwarzschild type of metric, is presented for the case where an isospin chemical potential is introduced. It turns out that the chemical potential stabilizes the behavior of the Skyrmion discussed previously in the literature. This analysis is carried on in the framework of a variational approach using different ansaetze for the radial profile of the Skyrmion. We found a divergent behavior for the size of the Skyrmion, associated to a certain critical value $\mu_c$ of the chemical potential. At this point, the mass of the Skyrmion vanishes. $\mu_c$ is essentialy independent of gravitating effects. The stability of a large N skyrmion against decays into single particles is also discussed.Comment: 10 pages, 4 figures Small changes to the previous version and a new referenc

The effects of quantum instantons on the thermodynamics of the CP^(N-1) model

Using the 1/N expansion, we study the influence of quantum instantons on the thermodynamics of the CP^(N-1) model in 1+1 dimensions. We do this by calculating the pressure to next-to-leading order in 1/N, without quantum instanton contributions. The fact that the CP^1 model is equivalent to the O(3) nonlinear sigma model, allows for a comparison to the full pressure up to 1/N^2 corrections for N=3. Assuming validity of the 1/N expansion for the CP^1 model makes it possible to argue that the pressure for intermediate temperatures is dominated by the effects of quantum instantons. A similar conclusion can be drawn for general N values by using the fact that the entropy should always be positive.Comment: 7 pages, 5 figures, revtex. To appear in PRD. Some arguments and conclusions reformulate

Applications of the Mellin-Barnes integral representation

We apply the Mellin-Barnes integral representation to several situations of interest in mathematical-physics. At the purely mathematical level, we derive useful asymptotic expansions of different zeta-functions and partition functions. These results are then employed in different topics of quantum field theory, which include the high-temperature expansion of the free energy of a scalar field in ultrastatic curved spacetime, the asymptotics of the $p$-brane density of states, and an explicit approach to the asymptotics of the determinants that appear in string theory.Comment: 20 pages, LaTe

Local Casimir Energies for a Thin Spherical Shell

The local Casimir energy density for a massless scalar field associated with step-function potentials in a 3+1 dimensional spherical geometry is considered. The potential is chosen to be zero except in a shell of thickness $\delta$, where it has height $h$, with the constraint $h\delta=1$. In the limit of zero thickness, an ideal $\delta$-function shell is recovered. The behavior of the energy density as the surface of the shell is approached is studied in both the strong and weak coupling regimes. The former case corresponds to the well-known Dirichlet shell limit. New results, which shed light on the nature of surface divergences and on the energy contained within the shell, are obtained in the weak coupling limit, and for a shell of finite thickness. In the case of zero thickness, the energy has a contribution not only from the local energy density, but from an energy term residing entirely on the surface. It is shown that the latter coincides with the integrated local energy density within the shell. We also study the dependence of local and global quantities on the conformal parameter. In particular new insight is provided on the reason for the divergence in the global Casimir energy in third order in the coupling.Comment: 16 pages, revtex 4, no figures. Major additions, clarifications, and corections, references adde

Complete High Temperature Expansions for One-Loop Finite Temperature Effects

We develop exact, simple closed form expressions for partition functions associated with relativistic bosons and fermions in odd spatial dimensions. These expressions, valid at high temperature, include the effects of a non-trivial Polyakov loop and generalize well-known high temperature expansions. The key technical point is the proof of a set of Bessel function identities which resum low temperature expansions into high temperature expansions. The complete expressions for these partition functions can be used to obtain one-loop finite temperature contributions to effective potentials, and thus free energies and pressures.Comment: 9 pages, RevTeX, no figures. To be published in Phys. Rev D. v2 has revised introduction and conclusions, plus a few typographical errors are corrected; v3 corrects one typ

Photon Propagation in Space-Time with a Compactified Spatial Dimension

The one-loop effects of vacuum polarization induced by untwisted fermions in QED in a nonsimply connected space-time with topology $S^{1}\times R^{3}$ are investigated. It is found that photon propagation in this system is anisotropic, appearing several massive photon modes and a superluminal transverse mode. For small compactification radius $a$, the superluminal velocity increases logarithmically with $a$. At low energies the photon masses lead to an effective confinement of the gauge fields into a (2+1)-dimensional manifold transverse to the compactified direction. The system shows a topologically induced directional superconductivity.Comment: 5 pages, to appear in PL

Thermal Pions at Finite Isospin Chemical Potential

The density corrections, in terms of the isospin chemical potential $\mu_I$, to the mass of the pions are studied in the framework of the SU(2) low energy effective chiral lagrangian. The pion decay constant $f_{\pi}(T, \mu_{I})$ is also analized. As a function of temperature for $\mu_I =0$, the mass remains quite stable, starting to grow for very high values of $T$, confirming previous results. However, there are interesting corrections to the mass when both effects (temperature and chemical potential) are simultaneously present. At zero temperature the $\pi ^{\pm}$ should condensate when $\mu_{I} = \mp m_{\pi}$. This is not longer valid anymore at finite $T$. The mass of the $\pi_0$ acquires also a non trivial dependence on $\mu_I$ due to the finite temperature.Comment: 13 pages, 5 figure