Equal-time two-point correlation functions in Coulomb gauge Yang–Mills theory

Abstract

We apply a functional perturbative approach to the calculation of the equal-time two-point correlation functions and the potential between static color charges to oneloop order in Coulomb gauge Yang-Mills theory. The functional approach proceeds through a solution of the Schrödinger equation for the vacuum wave functional to order g 2 and derives the equal-time correlation functions from a functional integral representation via new diagrammatic rules. We show that the results coincide with those obtained from the usual Lagrangian functional integral approach, extract the beta function, and determine the anomalous dimensions of the equal-time gluon and ghost two-point functions and the static potential under the assumption of multiplicative renormalizability to all orders. *

Hamiltonian flow in Coulomb gauge Yang-Mills theory

“…The same can be inferred from the diagrammatic analysis of Ref. [29] when extended to higher perturbative orders, if one takes into account that there are no nonlocal terms or higher couplings including ghost fields in the action (26). We stress again that scaling behavior does not necessarily imply confinement.…”

“…It has been confirmed on the nonperturbative level for the Landau gauge case in lattice studies [31]. As for the Coulomb gauge, a perturbative evaluation of the vertex (to one-loop level) at the symmetric point shows that the quantum corrections are finite and independent of the scale [29,32].…”

“…In Ref. [29], the vacuum functional has been determined explicitly to one-loop order through a perturbative solution of the Schrödinger equation for the ChristLee Hamiltonian. It was found that nonlocal terms in the couplings of two, three and four gluon fields in the wave functional give contributions to the static gluon propagator that are relevant to its ultraviolet behavior, in particular, its anomalous dimension.…”

“…To incorporate the appropriate initial conditions, it is convenient to cast the differential flow equations into an integral form, The initial conditions d à ðpÞ, ! à ðpÞ for the flow can be determined by perturbation theory [29,32]. Because of the kinematic structure of the ghost-gluon vertex no mass term for the ghost is produced.…”

Dimension two condensates in the Gribov-Zwanziger theory in Coulomb gauge

“…The resolution of the energy behaviour of this correlation function is a quite delicate point which requires a detailed mastering of the renormalization procedure of the Coulomb gauge. Here, we remind the reader to the large literature existing on this subject, both in the continuum as well as in the lattice formulation [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27].…”