Singularities in Forward Multiparticle Scattering Amplitudes and the S-Matrix Interpretation of Higher Virial Coefficients

Abstract

The role of singular forward multiparticle scattering amplitudes in S‐matrix formulas for the higher virial coefficients is studied in detail. It is shown that by means of a simple limiting process one can give a precise, unambiguous meaning to the traces over on‐shell scattering amplitudes which appear in our previous formulas for the virial coefficients. The general arguments, in which we maintain a reasonable level of rigor, are supported by explicit calculations for the third and fourth virial coefficients. Also, the angular momentum expansion used in earlier work is shown to converge.