Computer Algebra and Particle Physics 2005

Program

Abstracts of Lectures

[The lecture material is available here.]

• T. Binoth Multi-Leg Amplitudes at One Loop: Methods, Algorithms, Automatization and Numerics

  • Reduction procedures for one-loop multi-leg amplitudes

  • Algorithms for analytical and numerical evaluation of loop and phase space integrals

  • Implementation in FORM/MAPLE procedures

  • Automatic computation of a QCD one-loop amplitude

• J. Blümlein Harmonic Sums, Harmonic Polylogarithms and Special Functions

  • History of harmonic sums and harmonic polylogarithms in physics

  • Special Functions in higher loop computations and their algebraic properties

• M. Czakon Graph Theory Algorithms and Feynman Diagram Computations

  • Basic definitions, graph representations

  • Graph traversal, connectedness, shortest paths

  • QFT properties: 1PI, on-shell, etc.

  • Graph isomorphisms, symmetries and integrals

  • Graph generation

  • Examples libraries: QGRAF, DiaGen/IdSolver

• N. Glover Precision Phenomenology and Collider Physics

  • Phenomenology at present and future colliders

  • Precision predictions for HERA, Tevatron, LHC, ILC, ...

• T. Hahn Introduction to Mathematica and Cross Sections with FeynArts, FormCalc and Cuba

  • Basics of Mathematica

  • FeynArts, FormCalc 1-loop, (TwoCalc 2-loop) for standard model scattering processes

  • Numerical integration of cross-sections with Cuba lib

• R. Harlander Algebraic Methods for multi-loop Integrals

  • Integration by parts

  • Reduction of tensor integrals

  • Recurrence Relations: algorithms of Laporta, Baikov, Tarasov, ...

  • Expansions of Feynman integrals (thresholds, ...)

  • Solving large systems of linear equations

• A. Lorca Automation of Loop Calculations with Diana and aITALC

  • Introduction to QGRAF, DIANA, aITALC

  • Strategy and description of multimodular environment

  • Generating Feynman diagrams, extraction of amplitudes and kinematical variables

  • Control of numerical output, checks and tests

• S. Moch Symbolic Summation

  • Generalized hypergeometric functions in higher loops

  • Laurent expansion in small parameters and generalized nested sums

  • Recursive algorithms for symbolic summation

  • Examples libraries in FORM: Summer, XSummer

• J. Vermaseren Introduction to FORM

  • Getting started with FORM

  • Pattern matching

  • Patterns, functions and wildcards

  • Procedural Programming

  • Examples libraries: the FORM version of Mincer

• P. Wegner Parallel Computing

  • Hardware platforms for parallelization (PC-Clusters, SMP architectures, ...)

  • Basics of communication: Infiniband, MPI, ...

• S. Weinzierl Symbolic Computations in C++ and Introduction to GiNaC

  • Data structures: lists, containers, object-oriented design

  • Efficiency: shuffling, multiplication of large numbers, gcd, ...

  • Classical algorithms

  • Examples libraries: GiNaC

• S. Wiesand 64 bit on Linux - Status and perspectives

  • 64 bit technology, examples: AMD64 and EM64T

  • Performance for physics applications (ROOT, Phytia, FORM, ...)

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