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To obtain the second line in the above equation, we factorized the T operator into two vertex factors ''UV'' and ''W'', and inserted between them a sum over a complete set of intermediate exchanges ''R'' represented as plane waves moving along the ''-z'' axis. The upper vertex operator has been written as ''UV'' in anticipation of its further factorization into the primary resonance production operator ''V'' and its decay operator ''U''. Polarizations of all particles are represented by the reflectivity quantum numbers <math>\epsilon</math>. For the nucleon, the reflectivity is a complete description of its spin state. For reactions involving higher spin baryons, it would need to be supplemented by an additional <math>|m|</math> quantum number.
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To obtain the second line in the above equation, we factorized the T operator into two vertex factors ''UV'' and ''W'', and inserted between them a sum over a complete set of intermediate exchanges ''R'' represented as plane waves moving along the ''-z'' axis. The upper vertex operator has been written as ''UV'' in anticipation of its further factorization into the primary resonance production operator ''V'' and its decay operator ''U''. Polarizations of all particles are represented by their respective reflectivity quantum numbers <math>\epsilon</math>. For the nucleon, the reflectivity is a complete description of its spin state. For reactions involving higher spin baryons, it would need to be supplemented by an additional <math>|m|</math> quantum number.
     

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