Mathematical structures underlying the infravacuum picture of the electron

42nd LQP Workshop "Foundations and Constructive Aspects of QFT"
Wojciech Dybalski on June 22, 2018

We advance superselection theory of pure states on a C*-algebra beyond the conventional DHR setting. First, we canonically define conjugate and second-conjugate classes of such states w.r.t. a given reference `vacuum state’ and a `background automorphism’. Next, we identify a subset of backgrounds which take distinct sectors into one (second-)conjugate
class. We show that the Kraus-Polley-Reents infravacuum automorphisms fit into our framework and discuss consequences for the infrared problem in QED. Comparison with the approach of Kunhardt and with the concept of `charge classes’ of Buchholz and Roberts will also be given.