Studies On Some Problems In Constrained Hamilton System And Supersymmetry

This thesis reviews the historic research in constrained Hamilton system and progresses of gauge symmetry in constrained Hamilton system. We mainly discuss the canonical quantization procedure and Faddeev-Senjanovic path integral quantization procedure. We also introduce the symmetric properties of the canonical system. After checking the Dirac-Bergmann procedure in detail, we investigate the equivalence between the Dirac method and the matric method used by many references.We quantize the supersymmetric electrodynamics system based on both Faddeev-Senjanovic and Becchi-Rouet-Stora-Tyutin path integral quantization procedure. We construct the generator of gauge transformation and the generator of BRST transformation, then we obtain gauge transformation and BRST transformation of component fields, we find certain relations between the BRST generator and the gauge generator. Finally, we obtain the Ward-Takahashi identities according to the canonical Noether theorem, and discuss the relation between regular vertex and propagator. In the following, we quantize the supersymmetric anyon system according to the rule of path integral quantization for constrained Hamiltonian system in Faddeev-Senjanovic scheme. We calculate the quantal conserved angular momentum based on the quantal canonical Noether theorem, and present the fractional spin property at the quantum level.Based on above researches in supersymmetry, we proceed to investigate many applications of supersymmetry in cosmology and particle physics. We introduce supersymmetry and R parity, and discuss how supersymmetry is broken respectively in high and low energy scale. Besides that, we review the neutralino cosmology and the gravitino cosmology,and give the Tremaine-Gunn limit to the mass of dark matter particles.