The Soft Pomeron and Nonperturbative Corrections in Quark-Quark Scattering

We consider elastic quark-quark scattering at high energy with fixed momentum transfer $t$ and perform factorization of soft-gluon exchanges into a vacuum expectation value of Wilson lines. Taking into account nonperturbative corrections whose structure is predicted from infrared renormalon analysis, we represent the scattering amplitude as an asymptotic series. In the region of small momentum transfer, where the nonperturbative corrections are dominant, the scattering amplitude is Gaussian distribution in $t$ with a slope depending on a nonperturbative scale. A nonperturbative origin of the soft pomeron is thus identified.Comment: 18 pages, LaTeX styl

Rational, Replacement, and Local Invariants of a Group Action

The paper presents a new algorithmic construction of a finite generating set of rational invariants for the rational action of an algebraic group on the affine space. The construction provides an algebraic counterpart of the moving frame method in differential geometry. The generating set of rational invariants appears as the coefficients of a Groebner basis, reduction with respect to which allows to express a rational invariant in terms of the generators. The replacement invariants, introduced in the paper, are tuples of algebraic functions of the rational invariants. Any invariant, whether rational, algebraic or local, can be can be rewritten terms of replacement invariants by a simple substitution.Comment: 37 page

Baker-Akhiezer Modules on Rational Varieties

The free Baker-Akhiezer modules on rational varieties obtained from ${\mathbb C}P^{1}\times{\mathbb C}P^{n-1}$ by identification of two hypersurfaces are constructed. The corollary of this construction is the existence of embedding of meromorphic function ring with some fixed pole into the ring of matrix differential operators in $n$ variables