THE 3-GLUON VERTEX IN THE TEMPORAL-PLANAR GAUGE WITH THE LEIBBRANDT-VIENNA PRESCRIPTION - THE ONE-LOOP EFFECTIVE ACTION

The UV-divergent part of the one-loop contribution to the three-gluon vertex, Γμνρ{variant}abc, is computed in the temporal-planar gauge. The generalized Leibbrandt-Mandelstam (or Leibbrandt-Vienna) prescription - which is free from the inconsistencies that are known to affect the principal value prescription - is used to define the unphysical poles 1/(k·n)j. We compute the (one-loop) UV-divergent part of the gauge-field effective action up to order g3. We show that all the awkward non-local divergences can be written as the BRS variation of some functional X whereas the β-function coincides with the usual (covariant) result. In the homogeneous case we show that a non-local renormalization of the gauge field Aμa of the form A0μa = Zg- 1 2Aμa - h {combining short solidus overlay}f{hook}μa(A), A0μa and Aμa having identical gauge transformations, and the usual coupling constant renormalization, g0 = Zgμ2ε{lunate}g, suffice to get rid of all the UV-divergences in Γμνρ{variant}abc and the vacuum polarization tensor gPμνab. © 1990.