Aspects of Theories with Dynamical, Topological or Gauge Symmetries

Three topics are considered. Firstly, the so(2, 1) dynamical symmetry of a charged particle in the field of a vortex in 2 + 1 dimensions is used to solve the Schroedinger equation when an harmonic potential is present. Endowing the particle with a spin 1/2, we solve albraically the Pauli Hamiltonian in presence of a harmonic potential or a uniform magnetic field by identifying the representations of the ^l^*(2, 1) symmetry present in that case. Secondly, problems of topological field theories are discussed. Constructing explicitly the twisted N = 2 supersymmetry generators for the 3 + 1 dimensional topological Yang-Mills theory, we provide an understanding for the lack of local excitations of this theory. Working in 2 + 1 dimensions and defining a twist that also invert the Grassmann parity, abelian gauged fixed BF and Chern -Simons theories are obtained by twisting N = 4 supersymmetric matter Lagrangians. Analogous results are given in 1 + 1 dimensions. Thirdly, non-relativistic particles in thermal equilibrium are discussed in first quantization. The real time matrix propagator is recovered by making use of a parametrized form for the action. (Copies available exclusively from MIT Libraries, Rm. 14-0551, Cambridge, MA 02139-4307. Ph. 617 -253-5668; Fax 617-253-1690.).