Dorothea Bahns

The Effective Theory of Strings

We show that the Nambu–Goto string, and its higher dimensional generalizations, can be quantized, in the sense of an effective theory, in any dimension of the target space. The crucial point is to consider expansions around classical string configurations. We are using tools from perturbative algebraic quantum field theory, quantum field theory on curved spacetimes, and the Batalin–Vilkovisky formalism. Our model has some similarities with the Lüscher–Weisz string, but we allow for arbitrary classical background string configurations and keep the diffeomorphism invariance.

Schwinger Functions in Noncommutative Quantum Field Theory

It is shown that the n-point functions of scalar massive free fields on the noncommutative Minkowski space are distributions which are boundary values of analytic functions. Contrary to what one might expect, this construction does not provide a connection to the popular traditional Euclidean approach to noncommutative field theory (unless the time variable is assumed to commute). Instead, one finds Schwinger functions with twistings involving only momenta that are on the mass-shell. This explains why renormalization in the traditional Euclidean noncommutative framework crudely differs from renormalization in the Minkowskian regime.

Quantum Spacetime and Algebraic Quantum Field Theory

We review the investigations on the quantum structure of spacetime, to be found at the Planck scale if one takes into account the operational limitations to the localization of events which result from the concurrence of Quantum Mechanics and General Relativity. We also discuss the different approaches to (perturbative) Quantum Field Theory on Quantum Spacetime, and some of the possible cosmological consequences.

On-shell Extension of Distributions

We consider distributions on

Approximation von Funktionen

{\mathbb{R}^{n}{\setminus}\{0\}}

Ultraviolet Finiteness of the averaged Hamiltonian on the noncommutative Minkowski space

Rn\{0} which satisfy a given set of partial differential equations and provide criteria for the existence of extensions to

Local nets of von Neumann algebras in the Sine-Gordon model

{\mathbb{R}^n}