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

Abstract

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.

27 pages, 21 figures

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• Quark Sector of the QCD Groundstate in Coulomb Gauge
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• The ghost-gluon vertex in Hamiltonian Yang-Mills theory in Coulomb gauge
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• Dyson--Schwinger Approach to Hamiltonian QCD
• Dynamical Quark Mass Generation in QCD\textsubscript{3} within the Hamiltonian approach in Coulomb gauge
• Gauge-fixed Lattice QCD and the dispersion relation of Wilson fermions
• Deconfinement phase transition in the Hamiltonian approach to Yang-Mills theory in Coulomb gauge
• Hamiltonian approach to QCD in Coulomb gauge: Gribov's confinement scenario at work
• Ghost dynamics from Schwinger-Dyson equations
• Hamiltonian approach to QCD in Coulomb gauge at zero and finite temperature
• Hamiltonian approach to QCD in Coulomb gauge: From the vacuum to finite temperatures