vanishing connected time-ordered products
A theory of scattering for quasifree particles
Many theoretical physicists agree that is very difficult to construct and renormalize interacting quantum field theories using the framework of Wightman axioms. Some believe that it may be appropriate to start with an approximation, perhaps with some cut-off at large energy, so that modes with larger energy do not interact. Some physicists have generalized the Wightman framework. In particular, Streater points at questions related to a possible nonexistence of quantum electrodynamics in a strict sense. In his book he suggests a way around these problems, using unusual representations of the \(C^*\)-algebra of observables as inspired by Donaldson. Streater allows non-square integrability and so giving rise to a flat connection on the sheaf of electromagnetic fields, similar to the use of cocycles found by Doplicher and Roberts in the context of Haag-Kastler axioms. The main idea then is to introduce quasifree representations of the photon field. A quasifree quantum field is one with zero as the value of any connected time-ordered product of quantum fields. The book has eight chapters. Chapter 1 gives an introduction, Chapter 2 provides the Haag-Kastler Axioms, and Chapter 3 the representations of the Poincaré Group. Chapter 4 discusses the Maxwell Field, Chapter 5 certain representations, i.e. Weyl Relations, coherent states and the Segal-Bargmann Transform. Chapter 6 explains Euclidean Electrodynamics and the Nelson Axioms while Chapter 7 discusses certain models such as instantons, magnetic poles an solitons. A summary and conclusions may be found in Chapter 8.
scientific article; zbMATH DE number 6361943