The effective potential of the order parameter for confinement is calculated for $\mathrm{SU}(N)$ 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. Neglecting the ghost and using for the gluon energy $\omega (p)$ the approximate Gribov formula $\omega (p)\simeq p+M^2/p$ one finds a critical temperature of $\sqrt{3}M/\pi$. We explicitly show that the omission of the ghost drastically increases the transition temperature. From the full nonperturbative 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).

• Received 10 April 2013

DOI:https://doi.org/10.1103/PhysRevD.88.045024