General Lorentz-invariant representation of NN scattering amplitudes

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Abstract
A Lorentz-invariant representation for NN scattering amplitudes is derived. The general NN representation assuming parity invariance involves 128 amplitudes for a given isospin, all but 8 of which involve negative energy projection operators and therefore possess vanishing matrix elements in positive energy states. When charge symmetry and time-reversal invariance are taken into account, the number of independent amplitudes reduces to 56 for a given isospin, and this number further reduces to 44 when all particles are on mass shell. Relativistic meson theory is used to determine the negative energy terms since they cannot be determined from physical scattering data. The formalism is developed to determine the complete set of invariant amplitudes starting from partial wave t-matrix elements which arise from solving quasipotential equations for NN scattering.