Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2002-10-03
Physics
High Energy Physics
High Energy Physics - Theory
23 pages, LaTeX, no figures. V2: Presentation simplified and clarified, minor improvements in the whole text, typos corrected,
Scientific paper
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.
Gerdt Vladimir P.
Khvedelidze A. M.
Mladenov D. M.
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