Relativistic scattering operators for Dirac particles: Structure, symmetries, and reconstruction

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Abstract
A systematic construction of the general forms of relativistic scattering operators for spin-1/2 particles is presented. Lorentz-invariant two-body scattering operators for the spin-1/2-spin-1/2 and spin-1/2-spin-0 systems are explicitly represented in a manner which is the relativistic generalization of the Wolfenstein representation of Galilean-invariant scattering operators. The simpler spin-1/2-spin-0 case serves as a prototype for the much more complicated spin-1/2-spin-1/2 case. For each case a complete set of independent Lorentz invariants is obtained directly in terms of the available four-momenta and the Dirac γ matrices. The most general forms of the scattering operators are derived in terms of these.