Time development in the Schwinger model

In this thesis a reduction of the Schwinger model to a normal form has been presented. It was tried to approach the problem of the diagnolization directly. In the next step a procedure is given, by which the Hamilton operator can be transformed to a diagonal form. On the place of the unitarity goes the requirement for conservation of the commutator relations under the transformation. The transformation is then a scaling transformation, which diagonalizes the Hamilton operator not completely. The result of the transformation is a Jordan normal form. If the renormalization term is fixed by the requirement to obtain a massive excited state in the spectrum, then the Jordan normal form of the Hamilton operator has a one-dimensional 'Jordan block'. To this one-dimensional subspace a pair of together adjoint particle operators is assigned, which are the creation and annihilation operators of particles with the mass m=e/√π. These operators describe stationary states with positive norm. Beside the eigenvalue, which leads to a massive excited state, additionally a twofold degenerated eigenvalue for the mass zero exists. The particle operators belonging to this subspace are physically not interpretable. The operator pairs, the commutators of which are not zero, are not adjoint together. Furthermore they describe either no stationary states or their norm is not positive. Finally the time-development operator in the Schroedinger picture is given in a factorized form, which reflects immediately the physical interpretation. One factor describes the time development of the physical states, to further factors describe, completely decoupled from the first, the dynamics in an unphysical subspace. (orig./HSI)