Quantum gauge boson propagators in the light front

Gauge fields in the light front are traditionally addressed via the employment of an algebraic condition $n\cdot A=0$ in the Lagrangian density, where $A_{\mu}$ is the gauge field (Abelian or non-Abelian) and $n^\mu$ is the external, light-like, constant vector which defines the gauge proper. However, this condition though necessary is not sufficient to fix the gauge completely; there still remains a residual gauge freedom that must be addressed appropriately. To do this, we need to define the condition $(n\cdot A)(\partial \cdot A)=0$ with $n\cdot A=0=\partial \cdot A$. The implementation of this condition in the theory gives rise to a gauge boson propagator (in momentum space) leading to conspicuous non-local singularities of the type $(k\cdot n)^{-\alpha}$ where $\alpha=1,2$. These singularities must be conveniently treated, and by convenient we mean not only matemathically well-defined but physically sound and meaningfull as well. In calculating such a propagator for one and two noncovariant gauge bosons those singularities demand from the outset the use of a prescription such as the Mandelstam-Leibbrandt (ML) one. We show that the implementation of the ML prescription does not remove certain pathologies associated with zero modes. However we present a causal, singularity-softening prescription and show how to keep causality from being broken without the zero mode nuisance and letting only the propagation of physical degrees of freedom.Comment: 10 page

Feynman integrals with tensorial structure in the negative dimensional integration scheme

Negative dimensional integration method (NDIM) is revealing itself as a very useful technique for computing Feynman integrals, massless and/or massive, covariant and non-covariant alike. Up to now, however, the illustrative calculations done using such method are mostly covariant scalar integrals, without numerator factors. Here we show how those integrals with tensorial structures can also be handled with easiness and in a straightforward manner. However, contrary to the absence of significant features in the usual approach, here the NDIM also allows us to come across surprising unsuspected bonuses. In this line, we present two alternative ways of working out the integrals and illustrate them by taking the easiest Feynman integrals in this category that emerges in the computation of a standard one-loop self-energy diagram. One of the novel and as yet unsuspected bonus is that there are degeneracies in the way one can express the final result for the referred Feynman integral.Comment: 9 pages, revtex, no figure

Prepotential of N=2N=2 Supersymmetric Yang-Mills Theories in the Weak Coupling Region

We show how to obtain the explicite form of the low energy quantum effective action for $N=2$ supersymmetric Yang-Mills theory in the weak coupling region from the underlying hyperelliptic Riemann surface. This is achieved by evaluating the integral representation of the fields explicitly. We calculate the leading instanton corrections for the group SU(\nc), SO(N) and $SP(2N)$ and find that the one-instanton contribution of the prepotentials for the these group coincide with the one obtained recently by using the direct instanton caluculation.Comment: 13 pages, LaTe

A novel method to construct stationary solutions of the Vlasov-Maxwell system : the relativistic case

A method to derive stationary solutions of the relativistic Vlasov-Maxwell system is explored. In the non-relativistic case, a method using the Hermite polynomial series to describe the deviation from the Maxwell-Boltzmann distribution is found to be successful in deriving a few stationary solutions including two dimensional one. Instead of the Hermite polynomial series, two special orthogonal polynomial series, which are appropriate to expand the deviation from the Maxwell-J\"uttner distribution, are introduced in this paper. By applying this method, a new two-dimensional equilibrium is derived, which may provide an initial setup for investigations of three-dimensional relativistic collisionless reconnection of magnetic fields.Comment: 15pages, 2 figures, to appear in Phys. Plasma

Neutrino-12C scattering in the ab initio shell model with a realistic three-body interaction

We investigate cross sections for neutrino-12C exclusive scattering and for muon capture on 12C using wave functions obtained in the ab initio no-core shell model. In our parameter-free calculations with basis spaces up to the 6 hbarOmega we show that realistic nucleon-nucleon interactions, like e.g. the CD-Bonn, under predict the experimental cross sections by more than a factor of two. By including a realistic three-body interaction, Tucson-Melbourne TM'(99), the cross sections are enhanced significantly and a much better agreement with experiment is achieved. At the same time,the TM'(99) interaction improves the calculated level ordering in 12C. The comparison between the CD-Bonn and the three-body calculations provides strong confirmation for the need to include a realistic three-body interaction to account for the spin-orbit strength in p-shell nuclei.Comment: 6 pages, 2 figure

From the quantum Jacobi-Trudi and Giambelli formula to a nonlinear integral equation for thermodynamics of the higher spin Heisenberg model

We propose a nonlinear integral equation (NLIE) with only one unknown function, which gives the free energy of the integrable one dimensional Heisenberg model with arbitrary spin. In deriving the NLIE, the quantum Jacobi-Trudi and Giambelli formula (Bazhanov-Reshetikhin formula), which gives the solution of the T-system, plays an important role. In addition, we also calculate the high temperature expansion of the specific heat and the magnetic susceptibility.Comment: 18 pages, LaTeX; some explanations, 2 figures, one reference added; typos corrected; to appear in J. Phys. A: Math. Ge