Spinor Amplitudes in the Invariant Space: Analyticity, Unitarity, Crossing, and Constraints

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Abstract
The spinor amplitudes in the momentum space have simple properties in analyticity, unitarity, and crossing symmetry. For the purpose of dispersion analysis, it is more convenient to work in the space of the scalar invariants. However, by going over to the invariant space, kinematical singularities are introduced. We construct regularized spinor amplitudes which are free of any kinematical singularities, but not of kinematical zeros. The unitarity equation in terms of these amplitudes is derived explicitly. Their crossing relation is obtained and is simple. The merits and drawbacks of these spinor amplitudes are compared with those of the helicity amplitudes and of the invariant amplitudes. None of these formalisms is simple in all aspects of the dynamical and kinematical properties.