Relativistic extension of the Le Couteur-Newton formalism

Abstract

Assuming T-invariance and extended unitarity, we study in this paper a multichannel relativistic extension of the Le Couteur-Newton formalism (« determinantal method »). We prove that the two above-mentioned assumptions are entirely sufficient to work out a D/D formalism as a particular solution of the relativistic multichannel problem, having the same form as the nonrelativistic solution. We also prove in this case the existence of a new formalism, denoted B/B, for the multichannel reduced-reactance K-matrix. The 2n single-valued meromorphic functions $$B_\lambda \left( s \right)$$ give the multichannel K-matrix a structure, which is similar to the one given to the multichannel S-matrix, by the 2n values of the many-valued meromorphic function D(s). We also find and interpret over-determination relations between the values of the D-function on the various sheets, and similar ones for the $$B_\lambda $$ -functions. Finally, we prove that the D-function exists and we give a simple application of the B/B formalism.