Hello,

I am Carsten Schneider
 
 

You can reach me at

Research Institute for Symbolic Computation

J. Kepler University Linz
Altenbergerstraße 69
A-4040 Linz, Austria

Tel.: ++43 732 2468 9966
Fax: ++43 732 2468 9930
E-Mail: Carsten.Schneider@risc.uni-linz.ac.at

 
 
I am a member of the RISC combinatorics group.

Here is my list of publications.

My main research topic is

Multi-Summation in Difference Rings

The algorithms of the underlying summation theory of difference fields (PiSigma-fields) are implemented in the summation package Sigma.

Within this package one can

  • simplify nested sums (indefinite summation)
  • compute recurrences (Z's creative telescoping)
  • solve recurrences (with sum extensions)
All three components combined deliver strong tools in order to compute closed forms of summation problems. For more details see, e.g.,

C. Schneider. Symbolic Summation Assists Combinatorics. Sem. Lothar. Combin. 56, pp. 1-36. 2007. ISSN 1286-4889. Article B56b. [url] [ps] [pdf] [bib]

From 2008 on we apply these summation tools in particle physics:

Symbolic Summation in Perturbative Quantum Field Theory

In this interdisciplinary project we try to deal with challenging problems in the field of particle physics and perturbative quantum field theory with the help of our summation technology.
Generally speaking, the overall goal in particle physics is to study the basic elements of matter and the forces acting among them. The interaction of these particles can be described by the so called Feynman diagrams, respectively Feynman integrals. Then the crucial task is the concrete evaluation of these usually rather difficult integrals. In this way, one tries to obtain  additional insight how, e.g., the fundamental laws control the physical universe.

In cooperation with the combinatorics group (Peter Paule) at RISC and the theory group (Johannes Bluemlein) at Deutsches Elektronen-Synchrotron (DESY Zeuthen, a research centre of the German Helmholtz association), we are in the process of developing flexible and efficient summation and special function algorithms that assist in this task, i.e., simplification, verification and manipulation of Feynman integrals and sums, and of related expressions.
As it turns out, the software package Sigma plays one of the key roles: it is able to simplify highly complex summation expressions that typically arise within the evaluation of such Feynman integrals; see, e.g.,

  1. J. Bluemlein, M. Kauers, S. Klein, C. Schneider. Determining the closed forms of the {$O(a_s^3)$} anomalous dimensions and Wilson coefficients from Mellin moments by means of computer algebra. Comput. Phys. Comm. 180, pp. 2143-2165. 2009. [pdf] [bib]

  2. I. Bierenbaum, J. Bluemlein, S. Klein, C. Schneider. Two-Loop Massive Operator Matrix Elements for Unpolarized Heavy Flavor Production to $O(epsilon)$. Nucl.Phys. B 803(1-2), pp. 1-41. November 2008. ISSN: 0550-3213. [url] [pdf] [bib]

  3. S. Moch, C. Schneider. Feynman integrals and difference equations. In: Proc. ACAT 2007, PoS(ACAT)083, pp. 1-11. 2007. [url] [pdf] [bib]

  4. I. Bierenbaum, J. Blümlein, S. Klein, C. Schneider. Difference equations in massive higher order calculations. In: Proc. ACAT 2007, - (ed.)PoS(ACAT)082, pp. 1-15. 2007. ISSN 18248039. [url] [pdf] [bib]