We discuss the concept of what we refer to as semi-commuting linear differential operators. Such operators hold commuting operators as a special case. In particular, we discuss a heuristic by which one may construct such operators. Restricting to the case in which one such operator is of degree two, we construct families of linear differential operators semi-commuting with some named operators ...

The set of two partial differential equations for the Appell hypergeometric function in two variables F4(α, β, γ, α+ β − γ + 2 − h; x, y) is shown to arise as a null vector decoupling relation in a 2h-dimensional generalisation of the Coulomb gas model. It corresponds to a level two singular vector of an intrinsic Virasoro algebra. Dedicated to the memory of Mitko Stoyanov

Physical wave functions for the nucleon and the ∆+ isobar are presented, which unify the best features of previous models. With these wave functions we can calculate elastic form factors and the decays of the charmonium levels S1, P1, P2 into pp̄ in agreement with the data. A striking scaling behavior between R = |GM|/G p M and the coefficient B4 of the Appell polynomial decomposition of the nuc...

The purpose of this paper is to develop the theory of holomorphic gerbes on complex tori in a manner analogous to the classical theory for line bundles. In contrast to past studies on this subject, we do not restrict to the case where these gerbes are torsion, or even topologicaly trivial. We give an Appell-Humbert type description of all holomorphic gerbes on complex tori. This gives an explic...