Dyson-Schwinger Equations and Coulomb Gauge Yang-Mills Theory

Coulomb gauge Yang-Mills theory is considered within the first order formalism. It is shown that the action is invariant under both the standard BRS transform and an additional component. The Ward-Takahashi identity arising from this non-standard transform is shown to be automatically satisfied by the equations of motion.Comment: 3 pages, talk given at Quark Confinement and the Hadron Spectrum VII (2-7 Sep, 2006), Ponta Delgada, Azore

The ghost propagator in Coulomb gauge

We present results for a numerical study of the ghost propagator in Coulomb gauge whereby lattice results for the spatial gluon propagator are used as input to solving the ghost Dyson-Schwinger equation. We show that in order to solve completely, the ghost equation must be supplemented by a boundary condition (the value of the inverse ghost propagator dressing function at zero momentum) which determines if the solution is critical (zero value for the boundary condition) or subcritical (finite value). The various solutions exhibit a characteristic behavior where all curves follow the same (critical) solution when going from high to low momenta until `forced' to freeze out in the infrared to the value of the boundary condition. The boundary condition can be interpreted in terms of the Gribov gauge-fixing ambiguity; we also demonstrate that this is not connected to the renormalization. Further, the connection to the temporal gluon propagator and the infrared slavery picture of confinement is discussed.Comment: 3 pages, 2 figures, talk presented at "Quark Confinement and the Hadron Spectrum IX", Madrid, August 30-September 3, 2010, to appear in the proceeding

Schwinger-Dyson equations and disorder

Using simple models in D=0+0 and D=0+1 dimensions we construct partition functions and compute two-point correlations. The exact result is compared with saddle-point approximation and solutions of Schwinger-Dyson equations. When integrals are dominated by more than one saddle-point we find Schwinger-Dyson equations do not reproduce the correct results unless the action is first transformed into dual variables.Comment: 7 pages, 6 figure

Homogeneous TIP4P/2005 ice nucleation at low supercooling

We present a partial free energy profile for the homogeneous nucleation of ice using an all-atom model of water at low supercooling, at which ice growth dynamics are reasonably accessible to simulation. We demonstrate that the free energy profile is well described by classical nucleation theory, and that the nucleation barrier is entropic in origin. We also estimate to first order the temperature dependence of the interfacial free energy