Lorentz Invariant Multichannel Scattering Formalism

Abstract

A manifestly Lorentz invariant Hamiltonian formalism for multichannel scattering and production processes is developed by making two simple and natural extensions of the ordinary quantum mechanical formalism. The first is the asymptotic covariance postulate of Fong and Sucher which is essentially a necessary and sufficient condition for Lorentz invariance of the scattering amplitudes. The second is a Lorentz invariant extension of the asymptotic condition. It is shown that the latter is in fact no extension at all in a case where the total momentum operators of the asymptotic (unperturbed) systems are the same as the total momentum operators of the interacting system. In such a case the ordinary multichannel scattering formalism is completely Lorentz invariant whenever asymptotic covariance is satisfied.