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.