Anomaly Puzzle, Curved-Spacetime Spinor Hamiltonian, and String Phenomenology

In the first part of this dissertation, we study two different aspects of string phenomenology. First we discuss the complementary signals of low mass superstrings at the proposed electron-positron facilities (ILC and CLIC), in e+e- and {\gamma} {\gamma} collisions. We examine all relevant four-particle amplitudes evaluated at the center of mass energies near the mass of lightest Regge excitations and extract the corresponding pole terms. Secondly, we consider string realizations of the Randall-Sundrum effective theory and explore the search for the lowest massive Regge excitation of the gluon and of the extra (color singlet) gauge boson inherent of D-brane constructions. We also study the ratio of dijet mass spectra at small and large scattering angles. We show that with the first fb-1 such a ratio can probe lowest-lying Regge states for masses ~3.0 TeV. Finally, we propose that the 3.2$\sigma$ excess at about $140 {\rm GeV}$ in the dijet mass spectrum of $W$ + jets reproted by the CDF Collaboration originates in the decay of a leptophobic $Z'$ that can be related to the U(1) symmetries inherent of D-brane models. In the remaining parts of this dissertation, we discuss several points that may help to clarify some questions that remain about the anomaly puzzle in N=1 supersymmetric Yang-Mills theory and we investigate the issue that the Dirac Hamiltonian of a spin-1/2 particle in a curved background appears to be non-hermitian.