X iv : h ep - t h / 02 10 02 2 v 4 2 D ec 2 00 5 Light - cone SU ( 2 ) Yang - Mills theory and conformal mechanics

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.