Yang-Mills theory as Schrödinger quantum mechanics on the space of gauge-group orbits

Abstract

Recent proposals to study Yang-Mills theory on the space of gauge-group orbits are reconsidered. In particular, it is shown that the right formal Hamiltonian is not given by $\ensuremath{-}\frac{{\ensuremath{\hbar}}^{2}}{2}$ times the Laplace-Beltrami operator plus the standard "magnetic field" potential, as was suggested, but has an additional potential term proportional to ${\ensuremath{\hbar}}^{2}$ and is expressible in terms of the geometry not only of the space of gauge-group orbits but also of the orbits themselves as embedded in the space of gauge fields. Formal discussion of the continuum fields is substantiated by a rigorous consideration of lattice gauge theory.