144 research outputs found
Hamiltonian Approach to QCD: The effective potential of the Polyakov loop
The effective potential of the order parameter for confinement is calculated
within the Hamiltonian approach to Yang--Mills theory. Compactifying one
spatial dimension and using a background gauge fixing this potential is
obtained by minimizing the energy density for a given background field. Using
Gaussian type trial wave functionals I establish an analytic relation between
the propagators in the background gauge at finite temperature and the
corresponding zero temperature propagators in Coulomb gauge. In the simplest
truncation, neglecting the ghost and using the ultraviolet form of the gluon
energy one recovers the Weiss potential. From the fully non-perturbative
potential (with the ghost included) one extracts a critical temperature of the
deconfinement phase transition of 270 MeV for the gauge group SU(2).Comment: 8 pages, 6 eps figures. Talk given by Hugo Reinhardt at Xth Quark
Confinement and the Hadron Spectrum, October 8--12, 2012 TUM Campus Garching,
Munich, German
The effective potential of the confinement order parameter in the Hamiltonian approach
The effective potential of the order parameter for confinement is calculated
for SU(N) Yang--Mills theory in the Hamiltonian approach. Compactifying one
spatial dimension and using a background gauge fixing, this potential is
obtained within a variational approach by minimizing the energy density for
given background field. In this formulation the inverse length of the
compactified dimension represents the temperature. Using Gaussian trial wave
functionals we establish an analytic relation between the propagators in the
background gauge at finite temperature and the corresponding zero-temperature
propagators in Coulomb gauge. In the simplest truncation, neglecting the ghost
and using the ultraviolet form of the gluon energy, we recover the Weiss
potential. We explicitly show that the omission of the ghost drastically
increases the transition temperature. From the full non-perturbative potential
(with the ghost included) we extract a critical temperature of the
deconfinement phase transition of 269 MeV for the gauge group SU(2) and 283 MeV
for SU(3).Comment: 26 pages, 17 eps figure
Hamiltonian Dyson--Schwinger Equations of QCD
The general method for treating non-Gaussian wave functionals in the
Hamiltonian formulation of a quantum field theory, which was previously
developed and applied to Yang--Mills theory in Coulomb gauge, is generalized to
full QCD. The Hamiltonian Dyson-Schwinger equations as well as the quark and
gluon gap equations are derived and analysed in the IR and UV momentum regime.
The back-reaction of the quarks on the gluon sector is investigated.Comment: 7 pages, 3 eps figures. Talk given by D. Campagnari at Xth Quark
Confinement and the Hadron Spectrum, October 8--12, 2012 TUM Campus Garching,
Munich, German
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