Annihilation of singlet fermionic dark matter into two photons

We consider an extension of the standard model in which a singlet fermionic particle, to serve as cold dark matter, and a singlet Higgs are added. We perform a reanalysis on the free parameters. In particular, demanding a correct relic abundance of dark matter, we derive and plot the coupling of the singlet fermion with the singlet Higgs, $g_s$, versus the dark matter mass. We analytically compute the pair annihilation cross section of singlet fermionic dark matter into two photons. The thermally averaged of this cross section is calculated for wide range of energies and plotted versus dark matter mass using $g_s$ consistent with the relic abundance condition. We also compare our results with the Fermi-Lat observations.

A Renormalized perturbation theory for problems with nontrivial boundary conditions or backgrounds in two space-time dimensions

In this paper we discuss the effects of nontrivial boundary conditions or backgrounds, including non-perturbative ones, on the renormalization program for systems in two dimensions. Here we present an alternative renormalization procedure such that these non-perturbative conditions can be taken into account in a self-contained and, we believe, self-consistent manner. These conditions have profound effects on the properties of the system, in particular all of its $n$-point functions. To be concrete, we investigate these effects in the $lambda phi^4$ model in two dimensions and show that the mass counterterms turn out to be proportional to the Greens functions which have nontrivial position dependence in these cases. We then compute the difference between the mass counterterms in the presence and absence of these conditions. We find that in the case of nontrivial boundary conditions this difference is minimum between the boundaries and infinite on them. The minimum approaches zero when the boundaries go to infinity. In the case of nontrivial backgrounds, we consider the kink background and show that the difference is again small and localized around the kink.

A Direct Approach to the Electromagnetic Casimir Energy in a Rectangular Waveguide

In this paper we compute the leading order Casimir energy for the electromagnetic field (EM) in an open ended perfectly conducting rectangular waveguide in three spatial dimensions by a direct approach. For this purpose we first obtain the second quantized expression for the EM field with boundary conditions which would be appropriate for a waveguide. We then obtain the Casimir energy by two different procedures. Our main approach does not contain any analytic continuation techniques. The second approach involves the routine zeta function regularization along with some analytic continuation techniques. Our two approaches yield identical results. This energy has been calculated previously for the EM field in a rectangular waveguide using an indirect approach invoking analogies between EM fields and massless scalar fields, and using complicated analytic continuation techniques, and the results are identical to ours. We have also calculated the pressures on different sides and the total Casimir energy per unit length, and plotted these quantities as a function of the cross-sectional dimensions of the waveguide. We also present a physical discussion about the rather peculiar effect of the change in the sign of the pressures as a function of the shape of the cross-sectional area.

A new renormalization approach to the Dirichlet Casimir effect for phi^4 theory in (1+1) dimensions

The next to the leading order Casimir effect for a real scalar field, within $phi^4$ theory, confined between two parallel plates is calculated in one spatial dimension. Here we use the Greens function with the Dirichlet boundary condition on both walls. In this paper we introduce a systematic perturbation expansion in which the counterterms automatically turn out to be consistent with the boundary conditions. This will inevitably lead to nontrivial position dependence for physical quantities, as a manifestation of the breaking of the translational invariance. This is in contrast to the usual usage of the counterterms, in problems with nontrivial boundary conditions, which are either completely derived from the free cases or at most supplemented with the addition of counterterms only at the boundaries. We obtain emph{finite} results for the massive and massless cases, in sharp contrast to some of the other reported results. Secondly, and probably less importantly, we use a supplementary renormalization procedure in addition to the usual regularization and renormalization programs, which makes the usage of any analytic continuation techniques unnecessary.

The Dirichlet Casimir effect for $phi^4$ theory in (3+1) dimensions: A new renormalization approach

We calculate the next to the leading order Casimir effect for a real scalar field, within $phi^4$ theory, confined between two parallel plates in three spatial dimensions with the Dirichlet boundary condition. In this paper we introduce a systematic perturbation expansion in which the counterterms automatically turn out to be consistent with the boundary conditions. This will inevitably lead to nontrivial position dependence for physical quantities, as a manifestation of the breaking of the translational invariance. This is in contrast to the usual usage of the counterterms in problems with nontrivial boundary conditions, which are either completely derived from the free cases or at most supplemented with the addition of counterterms only at the boundaries. Our results for the massive and massless cases are different from those reported elsewhere. Secondly, and probably less importantly, we use a supplementary renormalization procedure, which makes the usage of any analytic continuation techniques unnecessary.