Narrow Results

We study the radiation of photons from a classical charged particle. We particularly consider a situation where the particle has a constant velocity in the distant past, then is accelerated, and then has a constant velocity in the distant future. Starting with no photons in the distant past we seek to characterize the quantum state of the photon field in the distant future. Working in the Coulomb gauge and in a $C^{\ast }$-algebra formulation, we give sharp conditions on whether this state is or is not in Fock space.

We study the color confinement of QCD with the Coulomb gauge in lattice simulations. The color-Coulomb instantaneous interaction in color-singlet channel causes a linearly rising potential at large distances. We also estimate the other color-channel forces for two-quark states, i.e. color-octet, color-sextet and color-antitriplet channels. Moreover we investigate the volume dependence of color-nonsinglet potentials on finite lattices.

The structure of linear energy divergences is analyzed on the example of one graph to three-loop order. Such dangerous divergences do cancel when all graphs are added, but next-to-leading divergences do not cancel out.

We study the static gluon and quark propagator of the Hamiltonian approach to quantum chromodynamics in Coulomb gauge in one-loop Rayleigh–Schrödinger perturbation theory. We show that the results agree with the equal-time limit of the four-dimensional propagators evaluated in the functional integral (Lagrangian) approach.

Over the last few years, Slavnov has proposed a formulation of quantum Yang–Mills theory in the Coulomb gauge which preserves simultaneously manifest Lorentz invariance and gauge invariance of the ghost field Lagrangian. This paper presents in detail some of the necessary calculations, i.e. those dealing with the functional integral for the S-matrix and its invariance under shifted gauge transformations. The extension of this formalism to quantum gravity in the Prentki gauge deserves consideration.

We report a numerical study of two-quark potentials depending on the color-irreducible representation of the SU(3) group by using a quenched-lattice QCD simulation with the Coulomb gauge in the confinement phase. In addition, we display preliminary numerical results for color-decomposed three-quark potentials.