No 1004 (00370)

Family name : Tarasov
Given name : Oleg 
Affiliation : DESY-Zeuthen
Abbreviation : Zeuthen
E-mail address : tarasov@ifh.de
Title : Application of Gr\"obner basis method to evaluation of Feynman diagrams
Authors : Oleg Tarasov
Abstract :
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{\large Application of Gr\"obner
	    basis method to evaluation
	      of
	     Feynman diagrams}
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\begin{abstract}
An algorithm for the reduction of massive Feynman integrals
with any number of loops and external momenta  to a minimal
 set of basic integrals is proposed. The method is based on the
new algorithm for evaluating tensor integrals,  representation
of generalized recurrence relations  for a given
kind of integrals as a linear system of PDEs and  the  reduction
of this system to a Gr\"obner basis or involutive system.
Basic integrals reveal as parametric derivatives of the
system in the standard form and the number of basic integrals
in the minimal set is determined by the dimension of the solution
space of the system of PDEs.
Other representations of recurrence relations are discussed.
Application of the method to two-loop  integrals  is considered.
\end{abstract}


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