Euler-Calogero-Moser system from SU(2) Yang-Mills theory

Abstract

The relation between SU(2) Yang-Mills mechanics, originated from the 4-dimensional SU(2) Yang-Mills theory under the supposition of spatial homogeneity of the gauge fields, and the Euler-Calogero-Moser model is discussed in the framework of Hamiltonian reduction. Two kinds of reductions of the degrees of freedom are considered: due to the gauge invariance and due to the discrete symmetry. In the former case, it is shown that after elimination of the gauge degrees of freedom from the SU(2) Yang-Mills mechanics the resulting unconstrained system represents the ID_3 Euler-Calogero-Moser model with an external fourth-order potential. Whereas in the latter, the IA_6 Euler-Calogero-Moser model embedded in an external potential is derived whose projection onto the invariant submanifold through the discrete symmetry coincides again with the SU(2) Yang-Mills mechanics. Based on this connection, the equations of motion of the SU(2) Yang-Mills mechanics in the limit of the zero coupling constant are presented in the Lax form.

Revtex, 14 pages, no figures. Abstract changed, strata analysis have been included, typos corrected, references added

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• Generalized Calogero-Moser-Sutherland models from geodesic motion on GL(n, R) group manifold
• Analysis of constraints in light-cone version of SU(2) Yang-Mills mechanics
• Light-cone SU(2) Yang-Mills theory and conformal mechanics
• On application of involutivity analysis of differential equations to constrained dynamical systems
• A Class of integrable Spin Calogero-Moser systems II: Exact Solvability
• Classical mechanics on GL(n, R) group and Euler-Calogero-Sutherland model