AG Mathematische Physik, Maximilian Duell (LMU München): N-Particle Scattering in Wedge-local Quantum Field Theories

Maximilian Duell (LMU München)

N-Particle Scattering in Wedge-local Quantum Field Theories

Abstract:
Wedge-local quantum field theories (wQFT) are a generalization of relativistic
local QFTs, in which observables can be localized in very large wedge-shaped
regions in space-time. It is long known that the wedge-local perspective
sometimes has theoretical advantages. Only more recently, (w)QFT models
describing non-trivial scattering reactions have been constructed directly in a
wedge-local framework by Lechner, Buchholz, Summers, and others. Such
constructions have provided non-trivial models also on four-dimensional
Minkowski space-time, whereas the corresponding construction problem for
interacting local QFT is still open.

On the other hand, Scattering theory in a wedge-local setting was previously
only developed up to the two-particle level and a generalization to higher
particle numbers was not expected for geometric reasons. In my talk I will
explain how to construct N-particle scattering states for massive particle in
wedge-local QFTs. Based on this construction, N-particle S-matrices, collision
cross sections, and other quantities of physical interest can be calculated
directly in wQFTs. To conclude I will also discuss more recent work, where this
scattering theory is applied to wQFTs obtained by a general deformation
construction of Buchholz, Lechner and Summers.

(Based on my PhD thesis and joint work with W. Dybalski)