Unitary R-Matrices: Representations of Deformations of the Braid Group Arising From The BMW Algebra And Racks

The research area of this project is an operator-algebraic approach to QFT, modelling physical observables as elements of C*- or von Neumann algebras, symmetries by group actions of such algebras and states by positive linear functionals on them. This formulation makes it possible to use advanced tools such as Tomita-Takesaki theory in a QFT context.