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

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

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

Thermal Pions ns Isospin Chemical Potential Effects

The density corrections, in terms of the isospin chemical potential $\mu_I$, to the mass of the pions are investigated in the framework of the SU(2) low energy effective chiral invariant lagrangian. As a function of temperature and $\mu_I =0$, the mass remains quite stable, starting to grow for very high values of $T$, confirming previous results. However, the dependence for a non-vanishing chemical potential turns out to be much more dramatic. In particular, 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 $\mu_I$ at finite $T$.Comment: 5 pages, 2 figures. To appear in the proceedings of the International High-Energy Physics Conference on Quantum Chromodynamics QCD02, Montpellier, 2-9 July (2002

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

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

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

Skyrmions, Hadrons and isospin chemical potential

Using the Hamiltonian formulation, in terms of collective variables, we explore the evolution of different skyrmionic parameters as function of the isospin chemical potential ($\mu$), such as the energy density, the charge density, the isoscalar radius and the isoscalar magnetic radius. We found that the radii start to grow very fast for $\mu \gtrsim 140$ MeV, suggesting the occurrence of a phase transition.Comment: 10 pages, 5 figure

Skyrme model and Isospin Chemical Potential

We discuss the stability of the Skyrmion solution in the presence of a finite isospin chemical potential $\mu$. Solving numerically the mass of the Skyrmion as function of $\mu$, we find a critical value $\mu_c=222.8$ MeV where the Skyrmion mass vanishes. We compare the exact numerical treatment with an analytical discussion based on a special shape for the profile of the Skyrmion due to Atiyah and Manton. The extension of this ansatz for finite $\mu$ works quite well for $\mu<121$ MeV. Then, for small values of $\mu$, where the analytical approach is valid, we consider the possibility of having an angular deformation for the Skyrmionic profile, which is possible for finite values of $\mu$. This is however, a small effect. Finally we introduce finite temperature corrections, which strength the instability induced by the chemical potential, finding the dependence of the critical temperature on $\mu$.Comment: 13 pages, 7 figure