The implications of exact conformal symmetry for the S matrix of spinless massless particles are studied. Explicit forms for the scattering amplitudes are obtained in configuration space. Differential conditions for conformal-invariant amplitudes are derived in momentum space. These are solved for the case of elastic two-body scattering and lead to an integral representation of the general two-body amplitude in terms of Lorentz scalars. The integral representation involves two arbitrary functions of two variables and four explicit quadratures. Further study of the four quadratures appears in appendices.
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Bali et al. (1969) studied this question.
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