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Some quantum field theories, such as the chiral SU(2) @ SU(2) theory, can have a dynamics invariant under a group .Y that is realized on a vacuum which is invariant only under a subgroup 3' of .V. These theories may be defined by scalar fields which are coordinates for the coset manifold Y/Z. They are thus non-polynomial theories on a symmetric space, with the group motions in this space described by a set of Killing vectors. We show how the Lagrange function may be constructed entirely from the Killing vectors. In particular, all physical quantities may be expressed in terms of the currents formed out of the Killing vectors. The current correlation functions do not exhibit the spurious wave function renormalizations which are encountered if ordinary Green's functions are computed. We illustrate the general method by calculating one-loop counter terms in a completely invariant fashion. An appendix describes in simple terms the general theory of symmetric spaces, which should prove useful in other contexts.
๐ SIMILAR VOLUMES
We investigate the solutions, by a determinental method, for a partial wave Bethe-Salpeter equation describing composite particle scattering and for its cross channel analog. We compare the behavior at s = -m of the leading angular momentum singularity from the Bethe-Salpeter equation with that of t