Two-loop contributions to the electromagnetic form factors are calculated in the kinematic regime close to the fermion-antifermion threshold. The results are presented in an expansion in the velocity β of the fermions in the c.m. frame up to next-to-next-to leading order in β. The existence of a new Coulomb singularity logarithmic in β, which is closely related to the O(α 2 ln α) corrections kn...

Questions of flux regulation in biological cells raise a renewed interest in the narrow escape problem. The determination of a higher order asymptotic expansion of the narrow escape time depends on determining the singularity behavior of the Neumann Green's function for the Laplacian in a three-dimensional (3D) domain with a Dirac mass on the boundary. In addition to the usual 3D Coulomb singul...

Low–energy limits of N=2 supersymmetric field theories in the Higgs branch are described in terms of a non–linear 4–dimensional σ– model on a hyperKähler target space, classically obtained as a hyper-Kähler quotient of the original flat hypermultiplet space by the gauge group. We review in a pedagogical way this construction, and illustrate it in various examples, with special attention given t...

We derive the exact effective superpotential in 4d, N = 1 supersymmetric SU(2) gauge theories with NA triplets and 2Nf doublets of matter superfields. We find the quantum vacua of these theories; the equations of motion (for NA = 1) can be reorganized into the singularity conditions of an elliptic curve. From the phase transition points to the Coulomb branch, we find the exact Abelian gauge cou...

We study the dynamics of denaturation bubbles in double-stranded DNA on the basis of the Poland-Scheraga model. We show that long time distributions for the survival of DNA bubbles and the size autocorrelation function can be derived from an asymptotic weak noise approach. In particular, below the melting temperature the bubble closure corresponds to a noisy finite time singularity. We demonstr...

The evaluation of the matrix elements of the Coulomb interaction in calculations using the Lippmann–Schwinger (or related) equations is complicated by the existence of a singularity in the integrand. One method of handling this singularity is to use a procedure commonly called the Lande subtraction. A procedure is outlined which relates the subtraction integrals to formulae involving the zeros ...

To search the infrared behaviour of the propagator in three dimensional QED ordinary perturbative method is not appropreate because of its bad infrared divergences[4].Assuming spectral representation and LSZ reduction formula,we evaluate the infrared behaviour or the mass singularity of the fermion propagator in three dimensional QED as in four dimension.In quenched case with bare photon mass w...

To search the infrared behaviour of the propagator in three dimensional QED ordinary perturbative method is not appropriate because of its bad infrared divergences[4].Assuming spectral representation and LSZ reduction formula,we evaluate the infrared behaviour or the mass singularity of the fermion propagator in three dimensional QED as in four dimension.In quenched case with bare photon mass w...

To search the infrared behaviour of the propagator in three dimensional QED ordinary perturbative method is not appropreate because of its bad infrared divergences[4].Assuming spectral representation and LSZ reduction formula,we evaluate the infrared behaviour or the mass singularity of the fermion propagator in three dimensional QED as in four dimension.In quenched case with bare photon mass w...