Renormalization in Coulomb gauge QCD

In the Coulomb gauge of QCD, the Hamiltonian contains a non-linear Christ-Lee term, which may alternatively be derived from a careful treatment of ambiguous Feynman integrals at 2-loop order. We investigate how and if UV divergences from higher order graphs can be consistently absorbed by renormalization of the Christ-Lee term. We find that they cannot.Comment: 23 pages, 26 figure

Renormalization of Wilson Operators in Minkowski space

We make some comments on the renormalization of Wilson operators (not just vacuum -expectation values of Wilson operators), and the features which arise in Minkowski space. If the Wilson loop contains a straight light-like segment, charge renormalization does not work in a simple graph-by-graph way; but does work when certain graphs are added together. We also verify that, in a simple example of a smooth loop in Minkowski space, the existence of pairs of points which are light-like separated does not cause any extra divergences.Comment: plain tex, 8 pages, 5 figures not include

Feynman rules for Coulomb gauge QCD

The Coulomb gauge in nonabelian gauge theories is attractive in principle, but beset with technical difficulties in perturbation theory. In addition to ordinary Feynman integrals, there are, at 2-loop order, Christ-Lee (CL) terms, derived either by correctly ordering the operators in the Hamiltonian, or by resolving ambiguous Feynman integrals. Renormalization theory depends on the subgraph structure of ordinary Feynamn graphs. The CL terms do not have subgraph structure. We show how to carry out enormalization in the presene of CL terms, by re-expressing these as `pseudo-Feynman' inegrals. We also explain how energy divergences cancel.Comment: 8 pages, 10 figue

Linear energy divergences in Coulomb gauge QCD

The structure of linear energy divergences is analysed on the example of one graph to 3-loop order. Such dangerous divergences do cancel when all graphs are added, but next to leading divergences do not cancel out.Comment: 6 pages, 1 figur

Trokutasta Wilsonova petlja u 1 + 1 dimenziji

We study the triangle Wilson loop in 2 + ǫ dimensions to order g 2 in the lightcone gauge with Mandelstam-Leibbrandt prescription. The complete result agrees with the calculation performed in the Feynman gauge. However, at intermediate stages the new ‘ambiguous’ terms of the form ω ǫ 2 −1 ǫ −1 appear which are not controlled by any sort of Ward identity.Proučavana je trokutasta Wilsonova petlja u 2 + ǫ dimenziji do reda g 2 u uvjetu svjetlosnog konusa i Mandelstam-Leibbrandtovoj preskripciji. Konačni rezultat slaže se s računom provedenim u Feynmanovom baždarnom uvjetu. Međutim u međukoracima pojavljuju se novi “proizvoljni” članovi oblika ω ǫ 2 −1 ǫ −1 koji ne podliježu kontroli Wardovih identiteta

The Gluon Propagator in the Coulomb Gauge

We give the results for all the one-loop propagators, including finite parts, in the Coulomb gauge. In finite parts we find new non-rational functions in addition to the single logarithms of the Feynman gauge. Of course, the two gauges must agree for any gauge invariant function. We revise the manuscript hep-th/0311118v2 and Eur.Phys.J.C37, 307-313(2004) in accordance with the notation and correct Feynman rules for the Coulomb gauge in Minkowski space found in [16]. The high-energy behaviour of the proper two-point functions is added in Appendix C.Comment: 14 pages, 9 figures, discussion extented, accepted for publication in Eur. Phys. J.

Wilsonova petlja i eksponentni teorem u uvjetu svjetlosnog konusa

Despite the fact that the Mandelstam-Leibbrandt prescription for the light-cone gauge fails to give CRCG terms correctly to order g4, it does give C2R terms which do agree with those in the Feynman gauge. Thus, the exponentiation theorem remains satisfied.Premda Mandelstam-Leibbrandtova preskripcija za uvjet svjetlosnog konusa ne daje C_RC_G članove korektne do reda g4 , članovi proporcionalni C2R slažu se s onima u Feynmanovom uvjetu. Tako je eksponentni teorem zadovoljen

Cancellation of energy-divergences in Coulomb gauge QCD

In the Coulomb gauge of nonabelian gauge theories there are in general, in individual graphs, 'energy-divergences' on integrating over the loop energy variable for fixed loop momentum. These divergences are avoided in the Hamiltonian, phase-space formulation. But, even in this formulation, energy-divergences re-appear at 2-loop order. We show in an example how these cancel between graphs as a consequence of Ward identities.Comment: 8 pages, 3 figures, revised version, two references added; accepted for publication in EPJ