Four-dimensional integration by parts with differential renormalization as a method of evaluation of Feynman diagrams

It is shown how strictly four-dimensional integration by parts combined with differential renormalization and its infrared analogue can be applied for calculation of Feynman diagrams.Comment: 6 pages, late

Determination of the pattern of nuclear binding from the data on the lepton-nucleus deep inelastic scattering

Nucleon structure function ratios r(x) = F2A(x)/F2D(x) measured in the range of atomic masses A larger or equal 4 are analyzed with the aim to determine the pattern of the x and A dependence of F2(x) modifications caused by nuclear environment. It is found that the x and A dependence of the deviations of the r(x) from unity can be factorized in the entire range of x. The characteristic feature of the factorization is represented with the three cross-over points x_i, i = 1 -- 3 in which r(x) = 1 independently of A. In the range x lager than 0.7 the pattern of r(x) is fixed with x_3 = 0.84 +/- 0.01. The pattern of the x dependence is compared with theoretical calculations of Burov, Molochkov and Smirnov to demonstrate that evolution of the nucleon structure as a function of A occurs in two steps, first for A less or equal 4 and second for A larger than 4. The long-standing problem of the origin of the EMC effect is understood as the modification of the nucleon structure in the field responsible for the binding forces in a three-nucleon system.Comment: Talk presented at INPC-99 Conference, Paris, August 24-28, 1998. 15 pages (LaTeX) including 6 figures which are generated from 22 postscript encapsulated figure

Nodal Domain Statistics for Quantum Maps, Percolation and SLE

We develop a percolation model for nodal domains in the eigenvectors of quantum chaotic torus maps. Our model follows directly from the assumption that the quantum maps are described by random matrix theory. Its accuracy in predicting statistical properties of the nodal domains is demonstrated by numerical computations for perturbed cat maps and supports the use of percolation theory to describe the wave functions of general hamiltonian systems, where the validity of the underlying assumptions is much less clear. We also demonstrate that the nodal domains of the perturbed cat maps obey the Cardy crossing formula and find evidence that the boundaries of the nodal domains are described by SLE with $\kappa$ close to the expected value of 6, suggesting that quantum chaotic wave functions may exhibit conformal invariance in the semiclassical limit.Comment: 4 pages, 5 figure

On the Resolution of Singularities of Multiple Mellin-Barnes Integrals

One of the two existing strategies of resolving singularities of multifold Mellin-Barnes integrals in the dimensional regularization parameter, or a parameter of the analytic regularization, is formulated in a modified form. The corresponding algorithm is implemented as a Mathematica code MBresolve.mComment: LaTeX, 10 page