[en] We look back at early efforts to approximate the large N_c Feynman diagrams of QCD as very large fishnet diagrams. We consider more carefully the uniqueness of rules for discretizing P⁺ and ix⁺ which fix the fishnet model in the strong 't Hooft coupling limit, and we offer some refinements that allow more of the crucial QCD interactions to be retained in the fishnet approximation. This new discretization has a better chance to lead to a physically sensible ''bare QCD string'' model. Not surprisingly the resulting fishnet diagrams are both richer in structure and harder to evaluate than those considered in older work. As warm-ups we analyze arbitrarily large fishnets of a paradigm scalar cubic theory and very small fishnets of QCD. (c) 2000 The American Physical Society

[en] A new method of massive Feynman diagrams calculation which is based on the rule of integration by parts is given. This rule is expanded to the massive case. The result of the application of the rule of integration by parts is the differential equation with respect to the mass for the initial diagram. The right hand side of the equation contains simple diagrams. 23 refs

[en] A slight modification of Feynman's original method leads to the Maslov correction in the path integral formula of a harmonic oscillator. Caustics are treated in a direct geometry way

[en] The singular behavior of the generic amplitude for a Feynman graph G, when one initially non-zero mass parameter vanishes, is investigated. It is shown that locally the amplitude decomposes as a sum of a regular part plus terms behaving like powers of the vanishing mass; the ''residues'' associated with various terms are identified with amplitudes for sub and quotient graphs of G

[en] Gauge mediated models of supersymmetry breaking often exhibit 'gaugino screening,' where to leading order in F, gaugino masses are unaffected by higher dimensional Kahler potential interactions between the supersymmetry breaking spurion and the messengers. We provide a derivation of this phenomenon which utilizes the gaugino counterterm originally proposed in the context of anomaly mediation by Dine and Seiberg. We argue that this counterterm is present when there are non-zero messenger F-terms, and can cancel the leading order Feynman diagram contribution to the gaugino mass. We provide a nontrivial check of the regulator independence of our results by performing the computation using both dimensional reduction and Pauli-Villars. This analysis reconciles an apparent contradiction between diagrammatics and analytic continuation into superspace.

[en] The physical aspects of the Glauber model problems are studied: potential model, profile function and Feynman diagrams approaches. Different generalizations of the Glauber model are discussed: particularly higher and lower energy processes and large angles

[en] A new method of massive Feynman diagram calculation which provides a fairly simple procedure of obtaining the result without the D-space (for the dimensional regularization) integrals calculation is presented. Different complicated diagrams are calculated as an illustration of the method capacities. 23 refs

[en] An automated treatment of iterated integrals based on letters induced by real-valued quadratic forms and Kummer-Poincaré letters is presented. These quantities emerge in analytic single and multi-scale Feynman diagram calculations. To compactify representations, one wishes to apply general properties of these quantities in computer-algebraic implementations. We provide the reduction to basis representations, expansions, analytic continuation and numerical evaluation of these quantities.

[en] A class of the renormalization schemes which are not based on subtraction of counterterms is described. In the schemes renormalized Feynman amplitude is constructed by the recurrent way from amplitudes without one inter line. It is shown that these renormalizations are equivalent to the R-operation of Bogolyubov-Parasyuk. 16 refs

[en] Vertex functions are calculated in the framework of differential equation method. As an example of calculation of one- and two-loop diagrams, it is shown that by analogy with propagator-type diagrams this method provides a simple procedure of evaluating the result without D- space integrals (for the dimensional regularization) calculation. 13 refs