Davide R. Campagnari

Non-Gaussian wave functionals in Coulomb gauge Yang-Mills theory

A general method to treat non-Gaussian vacuum wave functionals in the Hamiltonian formulation of a quantum field theory is presented. By means of Dyson-Schwinger techniques, the static Green functions are expressed in terms of the kernels arising in the Taylor expansion of the exponent of the vacuum wave functional. These kernels are then determined by minimizing the vacuum expectation value of the Hamiltonian. The method is applied to Yang-Mills theory in Coulomb gauge, using a vacuum wave functional whose exponent contains up to quartic terms in the gauge field. An estimate of the cubic and quartic interaction kernels is given using as input the gluon and ghost propagators found with a Gaussian wave functional.

Variational approach to Yang-Mills theory at finite temperatures

We study the finite-temperature phase of a gluon ensemble in a variational approximation to QCD in the Coulomb gauge. We derive and numerically solve the underlying Dyson-Schwinger equations up to one-loop order. Assuming the subcritical solution at T=0, we find a sharp transition in the infrared value of the gluon energy at a critical temperature.

Revised variational approach to QCD in Coulomb gauge

The variational approach to QCD in Coulomb gauge is revisited. By assuming the non-Abelian Coulomb potential to be given by the sum of its infrared and ultraviolet parts, i.e.~by a linearly rising potential and an ordinary Coulomb potential, and by using a Slater determinant ansatz for the quark wave functional, which contains the coupling of the quarks and the gluons with two different Dirac structures, we obtain variational equations for the kernels of the fermionic vacuum wave functional, which are free of ultraviolet divergences. Thereby, a Gaussian type wave functional is assumed for the gluonic part of the vacuum. By using the results of the pure Yang--Mills sector for the gluon propagator as input, we solve the equations for the fermionic kernels numerically and calculate the quark condensate and the effective quark mass in leading order. Assuming a value of

Vertex functions of Coulomb gauge Yang-Mills theory

\sigma_{\mathrm{C}} = 2.5 \sigma

The ghost–gluon vertex in Hamiltonian Yang–Mills theory in Coulomb gauge

for the Coulomb string tension (where

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

\sigma

Topological susceptibility in SU(2) Yang-Mills theory in the Hamiltonian approach in Coulomb gauge

is the usual Wilsonian string tension) the phenomenological value of the quark condensate

Hamiltonian Approach to QCD in Coulomb Gauge: A Survey of Recent Results

\langle \bar{\psi} \psi \rangle \simeq (-235 \, \mathrm{MeV})^3

Dyson--Schwinger approach to Hamiltonian Quantum Chromodynamics

is reproduced with a value of

Deconfinement phase transition in the Hamiltonian approach to Yang-Mills theory in Coulomb gauge

g \simeq 2.1