A Center-Symmetric 1/N Expansion

The free energy of U(N) gauge theory is expanded about a center-symmetric topological background configuration with vanishing action and vanishing Polyakov loops. We construct this background for SU(N) lattice gauge theory and show that it uniquely describes center-symmetric minimal action orbits in the limit of infinite lattice volume. The leading contribution to the free energy in the 1/N expansion about this background is of O(N^0) rather than O(N^2) as one finds when the center symmetry is spontaneously broken. The contribution of planar 't Hooft diagrams to the free energy is O(1/N^2) and sub-leading in this case. The change in behavior of the diagrammatic expansion is traced to Linde's observation that the usual perturbation series of non-Abelian gauge theories suffers from severe infrared divergences. This infrared problem does not arise in a center-symmetric expansion. The 't Hooft coupling \lambda=g^2 N is found to decrease proportional to 1/\ln(N) for large N. There is evidence of a vector-ghost in the planar truncation of the model.Comment: 27 pages, 2 figures; extended and corrected version with additional material and reference

An operatorial approach to stock markets

We propose and discuss some toy models of stock markets using the same operatorial approach adopted in quantum mechanics. Our models are suggested by the discrete nature of the number of shares and of the cash which are exchanged in a real market, and by the existence of conserved quantities, like the total number of shares or some linear combination of cash and shares. The same framework as the one used in the description of a gas of interacting bosons is adopted

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.

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

Casimir interaction energies for magneto-electric δ-function plates

We present boundary conditions for the electromagnetic fields on a δ-function plate, having both electric and magnetic properties, sandwiched between two magneto-electric semi-infinite half spaces. The optical properties for an isolated δ-function plate are shown to be independent of the longitudinal material properties of the plate. The Casimir-Polder energy between an isotropically polarizable atom and a magneto-electric δ-function plate is attractive for a purely electric δ-function plate, repulsive for a purely magnetic δ-function plate, and vanishes for the simultaneous perfect conductor limit of both electric and magnetic properties of the δ-function plate. The interaction energy between two identical δ-function plates is always attractive. It can be attractive or repulsive when the plates have electric and magnetic properties interchanged and reproduces Boyer’s result for the interaction energy between perfectly conducting electric and magnetic plates. The change in the Casimir-Polder energy in the presence of a δ-function plate on a magneto-electric substrate is substantial when the substrate is a weak dielectric