16 research outputs found
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
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.
Propagator in the Coulomb Gauge
The time-time component of the gluon propagator in the Coulomb gauge is
believed to provide a long-range confining force. We give the result, including
finite parts, for the propagator to order in the Coulomb
gauge.Comment: 5 pages, 4 figures, revised version, accepted for publication in
Europhysics Letter
The pinch technique at two-loops: The case of mass-less Yang-Mills theories
The generalization of the pinch technique beyond one loop is presented. It is
shown that the crucial physical principles of gauge-invariance, unitarity, and
gauge-fixing-parameter independence single out at two loops exactly the same
algorithm which has been used to define the pinch technique at one loop,
without any additional assumptions. The two-loop construction of the pinch
technique gluon self-energy, and quark-gluon vertex are carried out in detail
for the case of mass-less Yang-Mills theories, such as perturbative QCD. We
present two different but complementary derivations. First we carry out the
construction by directly rearranging two-loop diagrams. The analysis reveals
that, quite interestingly, the well-known one-loop correspondence between the
pinch technique and the background field method in the Feynman gauge persists
also at two-loops. The renormalization is discussed in detail, and is shown to
respect the aforementioned correspondence. Second, we present an absorptive
derivation, exploiting the unitarity of the -matrix and the underlying BRS
symmetry; at this stage we deal only with tree-level and one-loop physical
amplitudes. The gauge-invariant sub-amplitudes defined by means of this
absorptive construction correspond precisely to the imaginary parts of the
-point functions defined in the full two-loop derivation, thus furnishing a
highly non-trivial self-consistency check for the entire method. Various future
applications are briefly discussed.Comment: 29 pages, uses Revtex, 22 Figures in a separate ps fil