Repulsive long-range forces between anisotropic atoms and dielectrics

We investigate long-range forces between atoms with anisotropic electric polarizability interacting with dielectrics having anisotropic permittivity in the weak-coupling approximation. Unstable configurations in which the force between the objects is repulsive are constructed. Such configurations exist for three anisotropic atoms as well as for an anisotropic atom above a dielectric plate with a hole whose permittivity is anisotropic. Apart from the absolute magnitude of the force, the dependence on the configuration is qualitatively the same as for metallic objects for which the anisotropy is a purely geometric effect. In the weak limit closed analytic expressions for rather complicated configurations are obtained. The non-monotonic dependence of the interaction energy on separation is related to the fact that the electromagnetic Green's dyadic is not positive definite. The analysis in the weak limit is found to also semi-quantitatively explain the dependence of Casimir forces on the orientation of anisotropic dielectrics observed experimentally. Contrary to the scalar case, irreducible electromagnetic three-body energies can change sign. We trace this to the fact that the electromagnetic Green's dyadic is not positive definite.Comment: 9 page

Ghost Condensates and Dynamical Breaking of SL(2,R) in Yang-Mills in the Maximal Abelian Gauge

Ghost condensates of dimension two in SU(N) Yang-Mills theory quantized in the Maximal Abelian Gauge are discussed. These condensates turn out to be related to the dynamical breaking of the SL(2,R) symmetry present in this gaugeComment: 16 pages, LaTeX2e, final version to appear in J. Phys.

Many-Body Contributions to Green's Functions and Casimir Energies

The multiple scattering formalism is used to extract irreducible N-body parts of Green's functions and Casimir energies describing the interaction of N objects that are not necessarily mutually disjoint. The irreducible N-body scattering matrix is expressed in terms of single-body transition matrices. The irreducible N-body Casimir energy is the trace of the corresponding irreducible N-body part of the Green's function. This formalism requires the solution of a set of linear integral equations. The irreducible three-body Green's function and the corresponding Casimir energy of a massless scalar field interacting with potentials are obtained and evaluated for three parallel semitransparent plates. When Dirichlet boundary conditions are imposed on a plate the Green's function and Casimir energy decouple into contributions from two disjoint regions. We also consider weakly interacting triangular--and parabolic-wedges placed atop a Dirichlet plate. The irreducible three-body Casimir energy of a triangular--and parabolic-wedge is minimal when the shorter side of the wedge is perpendicular to the Dirichlet plate. The irreducible three-body contribution to the vacuum energy is finite and positive in all the cases studied.Comment: 22 pages, 8 figure

Electromagnetic semitransparent δ\delta-function plate: Casimir interaction energy between parallel infinitesimally thin plates

We derive boundary conditions for electromagnetic fields on a $\delta$-function plate. The optical properties of such a plate are shown to necessarily be anisotropic in that they only depend on the transverse properties of the plate. We unambiguously obtain the boundary conditions for a perfectly conducting $\delta$-function plate in the limit of infinite dielectric response. We show that a material does not "optically vanish" in the thin-plate limit. The thin-plate limit of a plasma slab of thickness $d$ with plasma frequency $\omega_p^2=\zeta_p/d$ reduces to a $\delta$-function plate for frequencies ($\omega=i\zeta$) satisfying $\zeta d \ll \sqrt{\zeta_p d} \ll 1$. We show that the Casimir interaction energy between two parallel perfectly conducting $\delta$-function plates is the same as that for parallel perfectly conducting slabs. Similarly, we show that the interaction energy between an atom and a perfect electrically conducting $\delta$-function plate is the usual Casimir-Polder energy, which is verified by considering the thin-plate limit of dielectric slabs. The "thick" and "thin" boundary conditions considered by Bordag are found to be identical in the sense that they lead to the same electromagnetic fields.Comment: 21 pages, 7 figures, references adde

Nonperturbative Gauge Fixing and Perturbation Theory

We compare the gauge-fixing approach proposed by Jona-Lasinio and Parrinello, and by Zwanziger (JPLZ) with the standard Fadeev-Popov procedure, and demonstrate perturbative equality of gauge-invariant quantities, up to irrelevant terms induced by the cutoff. We also show how a set of local, renormalizable Feynman rules can be constructed for the JPLZ procedure.Comment: 9 pages, latex, version to appear in Phys. Rev.

Semiclassical Casimir Energies at Finite Temperature

We study the dependence on the temperature T of Casimir effects for a range of systems, and in particular for a pair of ideal parallel conducting plates, separated by a vacuum. We study the Helmholtz free energy, combining Matsubara's formalism, in which the temperature appears as a periodic Euclidean fourth dimension of circumference 1/T, with the semiclassical periodic orbital approximation of Gutzwiller. By inspecting the known results for the Casimir energy at T=0 for a rectangular parallelepiped, one is led to guess at the expression for the free energy of two ideal parallel conductors without performing any calculation. The result is a new form for the free energy in terms of the lengths of periodic classical paths on a two-dimensional cylinder section. This expression for the free energy is equivalent to others that have been obtained in the literature. Slightly extending the domain of applicability of Gutzwiller's semiclassical periodic orbit approach, we evaluate the free energy at T>0 in terms of periodic classical paths in a four-dimensional cavity that is the tensor product of the original cavity and a circle. The validity of this approach is at present restricted to particular systems. We also discuss the origin of the classical form of the free energy at high temperatures.Comment: 17 pages, no figures, Late

Focusing Vacuum Fluctuations

The focusing of the vacuum modes of a quantized field by a parabolic mirror is investigated. We use a geometric optics approximation to calculate the energy density and mean squared field averages for scalar and electromagnetic fields near the focus. We find that these quantities grow as an inverse power of the distance to the focus. There is an attractive Casimir-Polder force on an atom which will draw it into the focus. Some estimates of the magnitude of the effects of this focusing indicate that it may be observable.Comment: 20 pages, 4 figures; typos corrected, two refs and some comments adde

Scale Anomaly Induced Instanton Interaction

The binary interaction of large size instantons in a SU(2) Yang-Mills theory is obtained from the one-loop effective action for the field strength. The instanton interaction is calculated as a function of the instanton separation and in dependence on radius and relative orientation of the instantons. Two equally oriented instantons with radii large compared with the scale defined by the gluon condensate have purely attractive interaction, whereas the interaction of maximal disoriented instantons is repulsive. We argue that the medium range attractive interaction of the instantons generally holds and is solely due to the instability of the perturbative vacuum.Comment: 11 LaTex pages (3 figures available on request), in press by Physics Letters B, UNITUE-THEP-4-199

Nambu-Jona-Lasinio Models Beyond the Mean Field Approximation

Inspired by the model of Nambu and Jona-Lasinio, various Lagrangians are considered for a system of interacting quarks. Employing standard techniques of many-body theory, the scalar part of the quark self-energy is calculated including terms up to second-order in the interaction. Results obtained for the single-particle Green's function are compared with those which only account for the mean-field or Hartree-Fock term in the self-energy. Depending on the explicit form of the Lagrangian, the second-order contributions range between 4 and 90 percent of the leading Hartree-Fock term. This leads to a considerable momentum dependence of the self-energy and the effective mass of the quarks.Comment: 17 page