A Laplace-Beltrami form for Yang-Mills theory

A brief introduction to some of the ideas of a gauge theory are presented w ith a review of the role of the path integral in developing a quantum theor y as well as the path integral over a space of the form S/G. The path integ ral of the gauge-invariant function over the space of inequivalent connecti ons under a given measure is discussed. It is shown that by taking the Yang -Mills Lagrangian, a formal quantum mechanical Hamiltonian in the space of gauge-invariant functionals can be derived. The scaler product is then give n by the formal Riemannian volume element on the space of orbits.