Jan Heffner

The effective potential of the confinement order parameter in the Hamiltonian approach

Abstract The effective potential of the order parameter for confinement is calculated within the Hamiltonian approach by compactifying one spatial dimension and using a background gauge fixing. Neglecting the ghost and using the perturbative gluon energy one recovers the Weiss potential. From the full non-perturbative potential calculated within a variational approach a critical temperature of the deconfinement phase transition of 269 MeV is found for the gauge group SU(2).

Covariant variational approach to Yang-Mills theory

We investigate the low-order Greens functions of SU(N) Yang-Mills theory in Landau gauge, using a covariant variational principle based on the effective action formalism. Employing an approximation to the Faddeev-Popov determinant established previously in the Hamiltonian approach in Coulomb gauge leads to a closed set of integral equations for the ghost and gluon propagator. We carry out the renormalization and the infrared analysis of this system of equations. Finally, we solve the renormalized system numerically and compare with lattice results and other functional approaches.

Finite-temperature Yang-Mills theory in the Hamiltonian approach in Coulomb gauge from a compactified spatial dimension

Yang-Mills theory is studied at finite temperature within the Hamiltonian approach in Coulomb gauge by means of the variational principle using a Gaussian-type Ansatz for the vacuum wave functional. Temperature is introduced by compactifying one spatial dimension. As a consequence the finite-temperature behavior is encoded in the vacuum wave functional calculated on the spatial manifold

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

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

where

Hamiltonian approach to QCD in Coulomb gauge at zero and finite temperature

{L}^{\ensuremath{-}1}

Hamiltonian approach to QCD in Coulomb gauge: From the vacuum to finite temperatures

is the temperature. The finite-temperature equations of motion are obtained by minimizing the vacuum energy density to two-loop order. We show analytically that these equations yield the correct zero-temperature limit while at infinite temperature they reduce to the equations of the

Hamiltonian Approach to QCD: The effective potential of the Polyakov loop

2+1

The deconfinement phase transition in the Hamiltonian approach to Yang–Mills theory in Coulomb gauge

-dimensional theory in accordance with dimensional reduction. The resulting propagators are compared to those obtained from the grand canonical ensemble where an additional Ansatz for the density matrix is required.

Hamilton approach to QCD in Coulomb gauge

We report on recent results obtained within the Hamiltonian approach to QCD in Coulomb gauge. Furthermore this approach is compared to recent lattice data, which were obtained by an alternative gauge-fixing method and which show an improved agreement with the continuum results. By relating the Gribov confinement scenario to the center vortex picture of confinement, it is shown that the Coulomb string tension is tied to the spatial string tension. For the quark sector, a vacuum wave functional is used which explicitly contains the coupling of the quarks to the transverse gluons and which results in variational equations which are free of ultraviolet divergences. The variational approach is extended to finite temperatures by compactifying a spatial dimension. The effective potential of the Polyakov loop is evaluated from the zero-temperature variational solution. For pure Yang–Mills theory, the deconfinement phase transition is found to be second order for and first order for , in agreement with the lattice results. The corresponding critical temperatures are found to be and , respectively. When quarks are included, the deconfinement transition turns into a crossover. From the dual and chiral quark condensate, one finds pseudocritical temperatures of and , respectively, for the deconfinement and chiral transition.