New light on infrared problems: sectors, statistics, symmetries and spectrum
The aim of this article is to shed new light on an old problem in quantum field theory, occurring in particular in QED where zero-mass photons give rise to infrared singularities in the context of perturbation theory. The mathematical framework used here has become known as \textit{algebraic quantum field theory} and has been developed by Doplicher, Haag and Roberts in 1969--1997. It has has proved to be a powerful tool for explaining the superselection structure and describing sectors of physical states. Still, so far one important class of theories is not covered by this framework, i.e. when there are forces mediated by massless particles like photons in QED. Quite unexpected, there seems to be a fundamental difference between theories describing only massive particles and theories including massless particles. In particular, the notion of superselection sector provides too fine a resolution of the state space, which leads to complications, and so the aim of the present investigation is to provide a slightly changed framework using concepts closer to actual experiments taking place in future directed light cones. Any such light cone \(V\) gives rise to an algebra of local observables in \(V\). One aspect of the present approach is the endomorphic nature of time evolution. The article has eight Sections. Section 1 provides the reader with a thorough discussion of modern tools, whereas the assumptions underlying the present analysis are presented in Section 2. In Section 3, the concept of \textit{vacuum in a light cone} is introduced and its charge class is analyzed. Section 4 establishes the concept of simple charge classes and derives their group structure and statistics. In Section 5, covariant charge classes are defined admitting unitary representations of the Poincaré group, while Section 6 is devoted to a proof of the spectrum condition. In Section 7, the relation between the present approach and the standard Minkowski space interpretation is discussed. The conclusions in Section 8 comment on the particle aspects of the present approach. I hope that these new results have the potential for solving real-world problems.
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