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Hamiltonian methods for nonlinear sigma models

Pak, Namık Kemal
Percacci, Roberto
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/H̄, where H̄ 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