Massless Asymptotic Fields and Haag–Ruelle Theory

Abstract

We revisit the problem of the existence of asymptotic massless boson fields in quantum field theory. The well-known construction of such fields by Buchholz (Commun. Math. Phys. 52:147–173, 1977; Commun. Math. Phys. 85:49–71, 1982) is based on locality and the existence of vacuum vector, at least in regions spacelike to spacelike cones. Our analysis does not depend on these assumptions and supplies a more general framework for fields only very weakly decaying in spacelike directions. In this setting, the existence of appropriate null asymptotes of fields is linked with their spectral properties in the neighborhood of the lightcone. The main technical tool is one of the results of a recent analysis by one of us (Herdegen in Lett. Math. Phys. 104:1263–1280. doi: 10.1007/s11005-014-0710-5 , 2014), which allows application of the null asymptotic limit separately to creation/annihilation parts of a wide class of nonlocal fields. In vacuum representation the scheme allows application of the methods of the Haag–Ruelle theory closely analogous to those of the massive case. In local case this Haag–Ruelle procedure may be combined with the Buchholz method, which leads to significant simplification.