Gluon self-interaction in the position space in Landau gauge

Details Gluon self-interaction in the position space in Landau gauge Gluon self-interaction in the position space in Landau gauge

2007-10-30

arxiv.org/abs/0710.5762v3

Int.J.Mod.Phys.A23:4145-4204,2008

Physics

High Energy Physics

High Energy Physics - Theory

47 pages, 1 figure, minor corrections, Eq. for J_31 on page 11 is corrected, to appear in Int. J. of Mod. Phys. A

Scientific paper

10.1142/S0217751X08040500

We propose a method to treat the three-gluon self-interaction vertex in the position space in D = 4 - 2e dimensions. As an example, we calculate a two-loop contribution to auxiliary Lcc vertex in the Landau gauge which contains the three-gluon vertex for SU(N) Yang-Mills theory. We represent the integral expression as a sum of separate contributions so that each of the contributions is a double finite integral or single integral (singular or finite) in the position space. In each double finite integral we use the freedom to shift exponents in powers in the denominator of integrands by some multiples of e, in order to perform at least one of the integrations by the uniqueness technique without corrupting the first term of the decomposition in e.

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