Symmetry principles in quantized systems

This thesis presents contributions to theoretical physics in the domain of quantum field theory and quantum Mechanics from work over the last fifteen years. A common thread running through the collection is the importance placed on symmetry principles in elucidating theoretical structures and constrainink physical predictions. Although the early work involves studies with conventional continuous symmetries (Lie groups), a predominant theme is supersymmetry, whose origins in relativistic field theory also date back about fifteen years. A major achievement of the present opus is perhaps the demonstration of the applicability of supersymmetry in contexts other than that of a relativistic spin symmetry. The papers exploring supersymmetric quantum mechanics, supersymmetry in nuclear and solid state physics, Becchi-RouetStora-Tyutin quantization supersymmetry, and internal supergroup gauging, all testify to this. The papers have been divided for review purposes onto five (overlapping) streams:- §S: spacetime (fermi-bose) supersymmetry; §M: physical models; §A: algebras and superalgebras; §Q: quantization and BRST supersymmetry; and §I: infinitedimensional symmetries. The collection, which forms the main body of the thesis, is preceded by a review covering each of these streams in turn. The main achievements and Most important papers are discussed, accompanied by a listing of the papers making up each stream. (Comments on relative contributions are also included for some co-authored works). Papers which overlap different streams are listed under each, and generally cross-referenced if they merit mentioning more than once. Within each review heading, papers are listed in chronological order of completion. The paper numbers refer to the main collection (also in chronological order of completion, but not disaggregated into streams). For ease of reference, a listing of the main collection is included as an index, together with the paper number and alphabetical stream identifier(s)