Constructions of Free Heterotic Parastring Theories and Partition Functions of Two Level Parastatistical Systems.

The first part of my dissertation deals with the constructions of free heterotic string theories in space -time dimensions of four and six by using parastatistics of order four and two respectively. The resulting four dimensional theory has a gauge group of Spin(8)/Z _2. The six dimensional theory has a gauge group of E_8. The mass spectrum of each of the theories contain bosons and fermions along with particles following exotic statistics. The second part of my dissertation deals with the statistical mechanics of systems following parastatistics, specifically, the constructions of partition functions of two level systems obeying parastatistics. These are the first non-trivial partition functions that exhibit the novelty of the statistical mechanics of systems following parastatistics. These partition functions have been compared to and contrasted with the partition functions of two level systems generated by the bose or the fermi statistics with or without internal symmetries.