Hamiltonian methods for nonlinear sigma models

Nonlinear sigma models are studied in n space dimensions with values in a coset space G/H as infinite dimensional Hamiltonian systems. An "intrinsic" formulation is discussed in terms of coordinates on G/H, an "embedded" formulation in terms of fields satisfying a constraint and a "lifted" formulation in terms of fields having values in G/H, where H is a normal subgroup of H. The coupling of the sigma model to Yang-Mills fields with structure group G is then considered, and it is shown that this system is equivalent to a massive Yang-Mills theory