Relativistische Materie in zwei Raum-Zeit-Dimensionen

Quantum field theory unifies concepts from quantum theory and from special relativity. Its mathematically rigorous description is quite intricate and is only partially understood; this is particularly true for the construction of operators corresponding to measurements at a space-time point or in a bounded space-time region. We explain this fact in simplified examples on 1+1 dimensional space-time, namely in so-called integrable models. We give a characterization of local operators by means of the analyticity properties of their coefficients in a certain series expansion. This also allows us to explicitly construct examples of local operators.