Solutions Of Classical Yang-Mills Equations Research Articles

First saturation correction in high energy proton-nucleus collisions. Part II. Single inclusive semi-hard gluon production

Exploiting recently obtained analytic solutions of classical Yang-Mills equations for higher order perturbations in the field of the dilute object (proton), we derive the complete first saturation correction to the single inclusive semi-hard gluon production in high energy proton-nucleus collisions by applying the Lehmann-Symanzik-Zimmermann reduction formula. We thus finalize the program started by Balitsky (see ref. [1]) and independently by Chirilli, Kovchegov and Wertepny (see ref. [2]) albeit using a very different approach to carry out our calculations. We extracted the functional dependence of gluon spectrum on the color charge densities of the colliding objects; thus our results can be used to evaluate complete first saturation correction to the double/multiple inclusive gluon productions.

On New Solutions of Classical Yang-Mills Equations with Cylindrical Sources

Strong fields generated by big electric currents are examined within the framework of the Yang-Mills nonlinear generalization of the Maxwell electrodynamics proposed in our earlier papers. First we consider the case of stationary currents and find a new exact solution to the Yang-Mills equations. Then we study a Yang-Mills field inside a thin circular cylinder with nonstationary plasma and find expressions for field strengths in it. Obtained results are applied to interpret several puzzling natural phenomena.

The instanton contributions to Yang-Mills theory on the torus: localization, Wilson loops and the perturbative expansion

The instanton contributions to the partition function and to homologically trivial Wilson loops for a U( N) Yang-Mills theory on a torus T 2 are analyzed. An exact expression for the partition function is obtained as a sum of contributions localized around the classical solutions of Yang-Mills equations, that appear according to the general classification of Atiyah and Bott. Explicit expressions for the exact Wilson loop averages are obtained when N = 2, N = 3. For general N the contribution of the zero-instanton sector has been carefully derived in the decompactification limit, reproducing the sum of the perturbative series on the plane, in which the light-cone gauge Yang-Mills propagator is prescribed according to Wu-Mandelstam-Leibbrandt (WML). Agreement with the results coming from S 2 is therefore obtained, confirming the truly perturbative nature of the WML computations.

On colour screening of classical Yang-Mills fields

By working in a temporal gauge the author shows that solutions of classical Yang-Mills equations with external charge and current densities with vanishing magnetic field may not be useful in explaining classical confinement.

Properties of Finite-Range Classical Solutions to Yang-Mills Theory

We study the classical solutions of Yang-Mills equations of motion where the field tensor ${G}_{\ensuremath{\mu}\ensuremath{\nu}}$ is assumed to decrease exponentially with $\mathcal{r}$, as $\mathcal{r}$, the spatial distance, goes to infinity. Sources are introduced and they are also assumed to decrease exponentially fast at infinity. We find that ${G}_{\ensuremath{\mu}\ensuremath{\nu}}$ has to decrease at least as fast as the sources at infinity. If we think that within a classical approach to confinement the size of the sources should not matter, then our result is an indication that quantum effects are necessary to achieve it.