2,269 research outputs found
Variational Approach to Yang--Mills Theory with non-Gaussian Wave Functionals
A general method for treating non-Gaussian wave functionals in quantum field
theory is presented and applied to the Hamiltonian approach to Yang-Mills
theory in Coulomb gauge in order to include a three-gluon kernel in the
exponential of the vacuum wave functional. The three-gluon vertex is calculated
using the propagators found in the variational approach with a Gaussian trial
wave functional as input.Comment: 3 pages, 4 figures, talk presented at "Quark Confinement and the
Hadron Spectrum IX", Madrid, August 30-September 3, 2010, to appear in the
proceeding
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.Comment: 27 pages, 21 figure
The deconfinement phase transition in the Hamiltonian approach to Yang--Mills theory in Coulomb gauge
The deconfinement phase transition of SU(2) Yang--Mills theory is
investigated in the Hamiltonian approach in Coulomb gauge assuming a
quasi-particle picture for the grand canonical gluon ensemble. The thermal
equilibrium state is found by minimizing the free energy with respect to the
quasi-gluon energy. Above the deconfinement phase transition the ghost form
factor remains infrared divergent but its infrared exponent is approximately
halved, while the gluon energy, being infrared divergent in the confined phase,
becomes infrared finite in the deconfined phase. For the effective gluon mass
we find a critical exponent of 0.37. Using the lattice results for the gluon
propagator to fix the scale, the deconfinement transition temperature is
obtained in the range of 275 to 290 MeV.Comment: 20 pages, 13 figures, accepted for publication by Phys. Rev.
Dyson--Schwinger Approach to Hamiltonian QCD
Dyson--Schwinger equations are an established, powerful non-perturbative tool
for QCD. In the Hamiltonian formulation of a quantum field theory they can be
used to perform variational calculations with non-Gaussian wave functionals. By
means of the DSEs the various -point functions, needed in expectation values
of observables like the Hamilton operator, can be thus expressed in terms of
the variational kernels of our trial ansatz. Equations of motion for these
variational kernels are derived by minimizing the energy density and solved
numerically.Comment: Talk given by D. Campagnari at XIIth Quark Confinement and the Hadron
Spectrum, August 28-September 04, 2016, Thessaloniki, Greece, submitted to
the proceeding
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.Comment: 11 pages, 6 eps figure
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