Local Operators in Massive Quantum Field Theories

A fundamental problem in quantum theory is to establish a connection between its local description (quantum field theory) and measurable quantities (particle masses, scattering amplitudes). In elementary particle physics one relies mostly on approximation techniques due to the non-integrable structure of the interactions. In order to gain a deeper understanding of quantum theory in general these issues are examined for integrable systems, where one hopes to gain exact relations between the two descriptions. Though many integrable theories in four dimensions are known (for a review see e.g. [1]) much more knowledge has been obtained so far for two dimensional theories, and it is thus this class of models where my investigations focus. In the particle picture the interaction is encoded into the scattering matrix. The asymptotic states are described by a linear superposition of free one-particle states |Zǫ(β)〉, which are characterised by the particle species ǫ and their momentum, parametrised as p = m cosh β, p = m sinh β (m denotes the mass and β the rapidity). They are related through the S-matrix as