Multiloop Feynman integrals and conformal quantum mechanics
Abstract
New algebraic approach to analytical calculations of Ddimensional integrals for multiloop Feynman diagrams is proposed. We show that the known analytical methods of evaluation of multiloop Feynman integrals, such as integration by parts and startriangle relation methods, can be drastically simplified by using this algebraic approach. To demonstrate the advantages of the algebraic method of analytical evaluation of multiloop Feynman diagrams, we calculate ladder diagrams for the massless φ^{3} theory. Using our algebraic approach we show that the problem of evaluation of special classes of Feynman diagrams reduces to the calculation of the Green functions for specific quantum mechanical problems. In particular, the integrals for ladder massless diagrams in the φ^{3} scalar field theory are given by the Green function for the conformal quantum mechanics.
 Publication:

Nuclear Physics B
 Pub Date:
 July 2003
 DOI:
 10.1016/S05503213(03)003936
 arXiv:
 arXiv:hepth/0303056
 Bibcode:
 2003NuPhB.662..461I
 Keywords:

 High Energy Physics  Theory;
 High Energy Physics  Phenomenology;
 Mathematical Physics
 EPrint:
 15 pages, Latex, corrected some typos and list of Refs