Interpretation of the asymptotic<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>S</mml:mi></mml:math>matrix for massless particles

Abstract

We discuss the existence and properties of the asymptotic $S$ matrix in field theories with massless particles. We show for the classic case of the scattering of an electron in an external electromagnetic field that the $S$-matrix method yields the same results as the traditional cross-section method involving properly formed sums over physically degenerate initial as well as final states. In that case, we show that observables are independent of the particular choice of asymptotic Hamiltonian. We argue that the massless theory is unique and discuss its relation to the massless limit of the massive theory. Although the results do not depend on it, a novel aspect of our formalism is the interpretation of physical states involving massless particles as Fock states and the occurrence of physical transitions in Fock space.