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Particles and Fields

Eur. Phys. J. C 19, 391-396
DOI: 10.1007/s100520100581

First results for the Coulomb gauge integrals using NDIM

A.T. Suzuki and A.G.M. Schmidt

Instituto de Física Teórica, Universidade Estadual Paulista, R. Pamplona, 145 São Paulo -SP CEP 01405-900 Brazil

(Received: 12 May 2000 / Revised version: 28 August 2000 / Published online: 15 March 2001 -© Springer-Verlag 2001)

The Coulomb gauge has at least two advantages over other gauge choices in that bound states between quarks and studies of confinement are easier to understand in this gauge. However, perturbative calculations, namely Feynman loop integrations, are not well defined (there are the so-called energy integrals) even within the context of dimensional regularization. Leibbrandt and Williams proposed a possible cure to such a problem by splitting the space-time dimension into $D=\omega+\rho$, i.e., introducing a specific parameter $\rho$ to regulate the energy integrals. The aim of our work is to apply the negative dimensional integration method (NDIM) to the Coulomb gauge integrals using the recipe of split-dimension parameters and present complete results -finite and divergent parts -to the one- and two-loop level for arbitrary exponents of the propagators and dimension.

© Società Italiana di Fisica, Springer-Verlag 2001