Rotational analyticity of the S matrix

Starting from known results of field theory, it is shown that both scattering and production amplitudes are analytic functions on the group SU(2). This analyticity is then used to simplify the derivation of high-energy bounds for scattering amplitudes of particles with spin. The origin of kinematic singularities as the result of parametrization of an analytic manifold is seen to be particularly transparent when the manifold is chosen to be SU(2). Field theory is used to show that production amplitudes are analytic in an SU(2) domain analogous to the Lehman ellipse for scattering amplitudes. Finally, unitarity is used to demonstrate that production amplitudes, when smeared over a small region of outgoing phase space, are SU(2) analytic in a larger domain analogous to the Martin ellipse.