Loop Equations for the d-dimensional One-Hermitian Matrix model

We derive the loop equations for the one Hermitian matrix model in any dimension. These are a consequence of the Schwinger-Dyson equations of the model. Moreover we show that in leading order of large $N$ the loop equations form a closed set.Comment: 13 pages, Latex, CERN-TH-6966/9

Mandelstam-Leibbrandt prescription

The light cone gauge is used frequently in string theory as well as gauge theories and gravitation. Loop integrals however have to be infrared regulated to remove spurious poles. The most popular and consistent of these infrared regulators is the Mandelstam-Leibbrandt(ML) prescription. The calculations with ML are rather cumbersome, though. In this work we show that the ML can be replaced by a symmetry of the regulator. This symmetry simplify the calculations, reducing them to conventional dimensional regularization integrals.Comment: Latex 7 page

Generation of interface for an Allen-Cahn equation with nonlinear diffusion

In this note, we consider a nonlinear diffusion equation with a bistable reaction term arising in population dynamics. Given a rather general initial data, we investigate its behavior for small times as the reaction coefficient tends to infinity: we prove a generation of interface property

Non-Abelian Antibrackets

The $\Delta$-operator of the Batalin-Vilkovisky formalism is the Hamiltonian BRST charge of Abelian shift transformations in the ghost momentum representation. We generalize this $\Delta$-operator, and its associated hierarchy of antibrackets, to that of an arbitrary non-Abelian and possibly open algebra of any rank. We comment on the possible application of this formalism to closed string field theory.Comment: LaTeX, 8 pages (minor modification