Internal affairs.

摘要

This thesis explores five topics in theoretical high energy physics. The first project involves the study of relationships between the wave functions at the origin for mesons composed of a heavy quark and a heavy anti-quark. Within the context of nonrelativistic potential models, we obtain several formulas (with varying degrees of rigor) relating the wave functions at the origin of the S-wave quarkonium systems containing b and c quarks. One of our main results is a model-independent relation which seems to hold to within 3.5% for any reasonable choice of interquark potential and any choice of radial quantum number. The second and third projects involve the study of bound states containing colored leptons. We study the spectra and decay widths of these states in the context of a nonrelativistic potential model which matches the recently calculated two-loop QCD potential at short distances to a successful phenomenological quarkonium potential at intermediate distances. We first considered bound states of heavy leptoquark-antiquark pairs (leptomesons) as well as leptoquark-antileptoquark pairs (leptoquarkonium). We then considered bound states of leptogluon-leptogluon pairs and show that under reasonable assumptions, the existence of one leptogluon flavor of appropriate mass can give rise to sizeable "leptoglueball" production rates and observable resonance peaks. The fourth project involves the study of pure Yang-Mills theories in two dimensions. In particular, we show that such theories are exactly solvable on a very general class of two-dimensional spacetimes---namely, 2-dimensional cell complexes---and that these spacetimes support a much richer class of theories than can exist on manifolds. The fifth project involves finding and classifying new forms of independent-particle quantum statistics obeying reasonable physical constraints in any number of spatial dimensions. Particles obeying a general statistics can be seen as having some number of internal degrees of freedom, some of which are bosonic and some of which are fermionic, each with some inherent fixed probability. This classification reduces to give the expected results in the physically realized Bose-Einstein and Fermi-Dirac limits.