Macrocausal aspects of the S matrix related to the LSZ asymptotic condition
H. D. Doebner, W. Lücke · Journal of Mathematical Physics · 1977
By use of the LSZ asymptotic condition in Hepp’s form it is shown that one may substitute functions s (x), which converge sufficiently rapidly to 1 in positive timelike direction, for the step function ϑ (x0) in the usual LSZ reduction formulas. This result, partly related to earlier work by Toll, does not depend on microcausality of the interpolating field. Choosing s (x) such that s (x) =0 outside the forward lightcone, a complete reduction to vacuum expectation values of T products of the interpolating field thus shows that it is sufficient to know the n-point Wightman distributions at pairwise timelike arguments x1,...,xn in order to calculate the S matrix completely. It is argued that this fact indicates some macrocausal property of the S matrix introduced by the LSZ asymptotic condition.