Physics – High Energy Physics – High Energy Physics - Phenomenology
Scientific paper
2004-02-18
Nucl.Instrum.Meth. A534 (2004) 279-283
Physics
High Energy Physics
High Energy Physics - Phenomenology
4 pages, 1 style file, to appear in the Proceedings of ACAT03, Tsukuba, Japan Refereces updated
Scientific paper
10.1016/j.nima.2004.07.101
The alternating and non-alternating harmonic sums and other algebraic objects of the same equivalence class are connected by algebraic relations which are induced by the product of these quantities and which depend on their index calss rather than on their value. We show how to find a basis of the associated algebra. The length of the basis $l$ is found to be $\leq 1/d$, where $d$ is the depth of the sums considered and is given by the 2nd {\sc Witt} formula. It can be also determined counting the {\sc Lyndon} words of the respective index set. The relations derived can be used to simplify results of higher order calculations in QED and QCD.
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