Abstract
The relation between the Euler-Calogero-Moser model and Yang-Mills mechanics, originating from the four-dimensional Yang-Mills theory under the supposition of spatial homogeneity of the gauge fields, is discussed in the framework of Hamiltonian reduction. Two kinds of reduction of the degrees of freedom are considered: due to gauge invariance and due to discrete symmetry. In the former case, it is shown that after elimination of the gauge degrees of freedom from the Yang-Mills mechanics the resulting unconstrained system represents the Euler-Calogero-Moser model with a certain external fourth-order potential. In the latter, the Euler-Calogero-Moser model embedded in a special external potential is considered, whose projection onto the invariant submanifold through the discrete symmetry coincides again with the Yang-Mills mechanics. Based on this connection, the equations of motion of the unconstrained Yang-Mills mechanics in the limit of zero coupling constant are presented in the Lax form.
- Received 27 July 2000
DOI:https://doi.org/10.1103/PhysRevD.62.125016
©2000 American Physical Society