On the temporal Wilson loop in the Hamiltonian approach in Coulomb gauge

Abstract

We investigate the temporal Wilson loop using the Hamiltonian approach to Yang-Mills theory. In simple cases such as the Abelian theory or the non-Abelian theory in (1+1) dimensions, the known results can be reproduced using unitary transformations to take care of time evolution. We show how Coulomb gauge can be used for an alternative solution if the exact ground state wave functional is known. In the most interesting case of Yang-Mills theory in (3+1) dimensions, the vacuum wave functional is not known, but recent variational approaches in Coulomb gauge give a decent approximation. We use this formulation to compute the temporal Wilson loop and find that the Wilson and Coulomb string tension agree within our approximation scheme. Possible improvements of these findings are briefly discussed.

24 pages, 4 eps-figures; new version matches published one

References in corpus (13)

• Confining Solution of the Dyson-Schwinger Equations in Coulomb Gauge
• Coulomb gauge gluon propagator and the Gribov formula
• Subcritical solution of the Yang-Mills Schroedinger equation in the Coulomb gauge
• Infrared analysis of propagators and vertices of Yang--Mills theory in Landau and Coulomb gauge
• Dielectric function of the QCD vacuum
• The effective Coulomb potential in SU(3) lattice Yang-Mills theory
• The 't Hooft loop in the Hamiltonian approach to Yang-Mills theory in Coulomb gauge
• BRST symmetry vs. Horizon condition in Yang-Mills theories
• Hamiltonian Approach to 1+1 dimensional Yang-Mills theory in Coulomb gauge
• The role of center vortices in Gribov's confinement scenario
• The Wilson loop from a Dyson equation
• Is the ground state of Yang-Mills theory Coulombic?
• Probing the ground state in gauge theories

Cited by in corpus (8)

• Perspective: Quantum Hamiltonians for Optical Interactions
• Running mass, effective energy and confinement: the lattice quark propagator in Coulomb gauge
• Coulomb vs. physical string tension on the lattice
• Ghost propagator and the Coulomb form factor from the lattice
• Gribov horizon and Gribov copies effect in lattice Coulomb gauge
• Heavy tetraquark confining potential in Coulomb gauge QCD
• Gauge-fixed Lattice QCD and the dispersion relation of Wilson fermions
• Lattice Coulomb propagators, effective energy and confinement