It has been known since the earliest days of quantum field theory (QFT) that infrared
divergences arise in scattering theory with massless fields. These infrared divergences are …

Stephen J. Gustafson Israel Michael Sigal Third Edition Page 1 Universitext Stephen J.
Gustafson Israel Michael Sigal Mathematical Concepts of Quantum Mechanics Third Edition …

Any nontrivial scattering with massless fields in four spacetime dimensions will generically
produce an out-state with memory. Scattering with any massless fields violates the standard …

A bstract A non-perturbative and exactly solvable quantum field theoretical model for a
“dressed Dirac field” is presented, that exhibits all the kinematical features of QED: an …

We propose a mathematically rigorous construction of the scattering matrix and the
interacting fields in models of relativistic perturbative quantum field theory with massless …

We extend the definition of asymptotic multiparticle states of the S-matrix beyond the tensor
products of one-particle states. We identify new quantum numbers called pairwise helicities …

We point out that recently published analyses of null and timelike infinity and long-range
structures in electrodynamics to large extent rediscover results present in the literature. At …

In this outline of a program, based on rigorous renormalization group theory, we introduce
new definitions which allow one to formulate precise mathematical conjectures related to …

We study the infrared problem in the usual model of quantum electrodynamics with
nonrelativistic matter. We prove spectral and regularity properties characterizing the mass …

The infrared problem in quantum electrodynamics consists of intriguing difficulties in
scattering theory appearing at large scales and low energies. Although they can be …