Light-cone SU(2) Yang-Mills theory and conformal mechanics

Gerdt, V. P.; Khvedelidze, A. M.; Mladenov, D. M.

Light-cone SU(2) Yang-Mills theory and conformal mechanics

Authors

Gerdt, V. P.

Khvedelidze, A. M.

Mladenov, D. M.

Description

We examine the mechanical matrix model that can be derived from the SU(2) Yang-Mills light-cone field theory by restricting the gauge fields to depend on the light-cone time alone. We use Dirac's generalized Hamiltonian approach. In contrast to its well-known instant-time counterpart the light-cone version of SU(2) Yang-Mills mechanics has in addition to the constraints, generating the SU(2) gauge transformations, the new first and second class constraints also. On account of all of these constraints a complete reduction in number of the degrees of freedom is performed. It is argued that the classical evolution of the unconstrained degrees of freedom is equivalent to a free one-dimensional particle dynamics. Considering the complex solutions to the second class constraints we show at this time that the unconstrained Hamiltonian system represents the well-known model of conformal mechanics with a ``strength'' of the inverse square interaction determined by the value of the gauge field spin.
23 pages, LaTeX, no figures. V2: Presentation simplified and clarified, minor improvements in the whole text, typos corrected, references added. V3: Very small changes. V4: Changes in the text, Appendix added, references added