Uses of zeta regularization in QFT with boundary conditions: a cosmo-topological Casimir effect

Zeta regularization has proven to be a powerful and reliable tool for the regularization of the vacuum energy density in ideal situations. With the Hadamard complement, it has been shown to provide finite (and meaningful) answers too in more involved cases, as when imposing physical boundary conditions (BCs) in two-- and higher--dimensional surfaces (being able to mimic, in a very convenient way, other {\it ad hoc} cut-offs, as non-zero depths). What we have considered is the {\it additional} contribution to the cc coming from the non-trivial topology of space or from specific boundary conditions imposed on braneworld models (kind of cosmological Casimir effects). Assuming someone will be able to prove (some day) that the ground value of the cc is zero, as many had suspected until very recently, we will then be left with this incremental value coming from the topology or BCs. We show that this value can have the correct order of magnitude in a number of quite reasonable models involving small and large compactified scales and/or brane BCs, and supergravitons.Comment: 9 pages, 1 figure, Talk given at the Seventh International Workshop Quantum Field Theory under the Influence of External Conditions, QFEXT'05, Barcelona, September 5-9, 200

The ground state energy of a massive scalar field in the background of a semi-transparent spherical shell

We calculate the zero point energy of a massive scalar field in the background of an infinitely thin spherical shell given by a potential of the delta function type. We use zeta functional regularization and express the regularized ground state energy in terms of the Jost function of the related scattering problem. Then we find the corresponding heat kernel coefficients and perform the renormalization, imposing the normalization condition that the ground state energy vanishes when the mass of the quantum field becomes large. Finally the ground state energy is calculated numerically. Corresponding plots are given for different values of the strength of the background potential, for both attractive and repulsive potentials.Comment: 15 pages, 5 figure

An analysis of the phase space of Horava-Lifshitz cosmologies

Using the dynamical system approach, properties of cosmological models based on the Horava-Lifshitz gravity are systematically studied. In particular, the cosmological phase space of the Horava-Lifshitz model is characterized. The analysis allows to compare some key physical consequences of the imposition (or not) of detailed balance. A result of the investigation is that in the detailed balance case one of the attractors in the theory corresponds to an oscillatory behavior. Such oscillations can be associated to a bouncing universe, as previously described by Brandenberger, and will prevent a possible evolution towards a de Sitter universe. Other results obtained show that the cosmological models generated by Horava-Lifshitz gravity without the detailed balance assumption have indeed the potential to describe the transition between the Friedmann and the dark energy eras. The whole analysis leads to the plausible conclusion that a cosmology compatible with the present observations of the universe can be achieved only if the detailed balance condition is broken.Comment: 12 pages, some typos corrected, some references adde

Market Definition with Differentiated Products: A Spatial Competition Application

This paper applies the ‘hypothetical monopolist’ test of market definition to a retail market with products differentiated by means of location and other dimensions. The test for defining the relevant product and geographic market follows the conditions required by the European Union Competition Law and so it takes into account both demand- and supply-side substitution. The empirical model using sales data from a set of movie theatres in the North of Spain, incorporating the observed locations of consumers vis-àvis the stores, shows that empirical tests of market definition may lead to an implausible definition of the relevant market if supply-side substitution is not accounted for

The Address Approach to Horizontal Product Differentiation: A Survey

The problem of non-existence of perfect equilibrium in the original model of Harold Hotelling and the principle of minimum differentiation he suggested have been tackled on different grounds. This paper provides a survey on the address approach to horizontal product differentiation and the different ways that works after Hotelling solved the problem of non-existence of perfect equilibrium by changing some of the assumptions of the model

Effective Finite Temperature Partition Function for Fields on Non-Commutative Flat Manifolds

The first quantum correction to the finite temperature partition function for a self-interacting massless scalar field on a $D-$dimensional flat manifold with $p$ non-commutative extra dimensions is evaluated by means of dimensional regularization, suplemented with zeta-function techniques. It is found that the zeta function associated with the effective one-loop operator may be nonregular at the origin. The important issue of the determination of the regularized vacuum energy, namely the first quantum correction to the energy in such case is discussed.Comment: amslatex, 14 pages, to appear in Phys. Rev.