12,948 research outputs found

    FIRE4, LiteRed and accompanying tools to solve integration by parts relations

    Full text link
    New features of the Mathematica code FIRE are presented. In particular, it can be applied together with the recently developed code LiteRed by Lee in order to provide an integration by parts reduction to master integrals for quite complicated families of Feynman integrals. As as an example, we consider four-loop massless propagator integrals for which LiteRed provides reduction rules and FIRE assists to apply these rules. So, as a by-product one obtains a four-loop variant of the well-known three-loop computer code MINCER. We also describe various ways to find additional relations between master integrals for several families of Feynman integrals

    On the reduction of Feynman integrals to master integrals

    Full text link
    The reduction of Feynman integrals to master integrals is an algebraic problem that requires algorithmic approaches at the modern level of calculations. Straightforward applications of the classical Buchberger algorithm to construct Groebner bases seem to be inefficient. An essential modification designed especially for this problem has been worked out. It has been already applied in two- and three-loop calculations. We are also suggesting to combine our method with the Laporta's algorithm.Comment: 8 pages, proceedings of ACAT0

    Gauge-Invariant Differential Renormalization: Abelian Case

    Get PDF
    A new version of differential renormalization is presented. It is based on pulling out certain differential operators and introducing a logarithmic dependence into diagrams. It can be defined either in coordinate or momentum space, the latter being more flexible for treating tadpoles and diagrams where insertion of counterterms generates tadpoles. Within this version, gauge invariance is automatically preserved to all orders in Abelian case. Since differential renormalization is a strictly four-dimensional renormalization scheme it looks preferable for application in each situation when dimensional renormalization meets difficulties, especially, in theories with chiral and super symmetries. The calculation of the ABJ triangle anomaly is given as an example to demonstrate simplicity of calculations within the presented version of differential renormalization.Comment: 15 pages, late

    The static quark potential to three loops in perturbation theory

    Full text link
    The static potential constitutes a fundamental quantity of Quantum Chromodynamics. It has recently been evaluated to three-loop accuracy. In this contribution we provide details on the calculation and present results for the 14 master integrals which contain a massless one-loop insertion.Comment: 6 pages, talk presented at Loops and Legs in Quantum Field Theory 2010, W\"orlitz, Germany, April 25-30, 201

    Asymptotic Expansions of Feynman Diagrams on the Mass Shell in Momenta and Masses

    Get PDF
    Explicit formulae for asymptotic expansions of Feynman diagrams in typical limits of momenta and masses with external legs on the mass shell are presented.Comment: 10 pages, LaTeX, final version to appear in Phys.Lett.

    Differential Renormalization, the Action Principle and Renormalization Group Calculations

    Full text link
    General prescriptions of differential renormalization are presented. It is shown that renormalization group functions are straightforwardly expressed through some constants that naturally arise within this approach. The status of the action principle in the framework of differential renormalization is discussed.Comment: 23 pages, late

    `Strategy of Regions': Expansions of Feynman Diagrams both in Euclidean and Pseudo-Euclidean Regimes

    Get PDF
    The strategy of regions [1] turns out to be a universal method for expanding Feynman integrals in various limits of momenta and masses. This strategy is reviewed and illustrated through numerous examples. In the case of typically Euclidean limits it is equivalent to well-known prescriptions within the strategy of subgraphs. For regimes typical for Minkowski space, where the strategy of subgraphs has not yet been developed, the strategy of regions is characterized in the case of threshold limit, Sudakov limit and Regge limit.Comment: 17 pages, LaTeX with axodraw.sty; Invited talk at RADCOR 2000 (Carmel CA, USA, Sept. 2000

    Factorization of Darboux-Laplace transformations for discrete hyperbolic operatros

    Full text link
    Elementary Darboux--Laplace transformations for semidiscrete and discrete second order hyperbolic operators are classified. It is proved that in the (semi)-discrete case there are two types of elementary Darboux--Laplace transformations as well: Darboux transformations that are defined by the choice of particular element in the kernel of the initial hyperbolic operator and classical Laplace transformations that are defined by the operator itself. It is proved that in the discrete case on the level of equivalence classes any Darboux--Laplace transformation is a product of elementary ones.Comment: 16 page

    Stasheff structures and differentials of the Adams spectral sequence

    Full text link
    The Adams spectral sequence was invented by J.F.Adams almost fifty years ago for calculations of stable homotopy groups of topological spaces and in particular of spheres. The calculation of differentials of this spectral sequence is one of the most difficult problem of Algebraic Topology. Here we consider an approach to solve this problem in the case of Z/2 coefficients and find inductive formulas for the differentials. It is based on the Stasheff algebra structures, operad methods and functional homology operations.Comment: 31 page

    Dynamic Transposition of Melodic Sequences on Digital Devices

    Full text link
    A method is proposed which enables one to produce musical compositions by using transposition in place of harmonic progression. A transposition scale is introduced to provide a set of intervals commensurate with the musical scale, such as chromatic or just intonation scales. A sequence of intervals selected from the transposition scale is used to shift instrument frequency at predefined times during the composition which serves as a harmonic sequence of a composition. A transposition sequence constructed in such a way can be extended to a hierarchy of sequences. The fundamental sound frequency of an instrument is obtained as a product of the base frequency, instrument key factor, and a cumulative product of respective factors from all the harmonic sequences. The multiplication factors are selected from subsets of rational numbers, which form instrument scales and transposition scales of different levels. Each harmonic sequence can be related to its own transposition scale, or a single scale can be used for all levels. When composing for an orchestra of instruments, harmonic sequences and instrument scales can be assigned independently to each musical instrument. The method solves the problem of using just intonation scale across multiple octaves as well as simplifies writing of instrument scores.Comment: 13 pages, 5 figures, 3 music sample
    • …
    corecore