Chad Davis with  Glenn Starkman

Higher Spin Wave Equations on Compact Hyperbolic Manifolds and Applications

Much attention has been paid recently to the possibility of extra dimensions, most of it in the context of “extra” flat toroidal factors to the space-time manifold; however, compact hyperbolic factors have recently been shown to possess attractive features.  In order to understand the detailed phenomenological implications of these compact hyperbolic manifolds (CHMs) for phenomena as varied as super-symmetry breaking and  the stabilizing effects of Casimir energy density, it will be necessary to compute the spectrum and wave-functions of excitations of fundamental fields in this geometry and with these boundary conditions. The challenge lies in the chaotic nature of dynamics on these manifolds which precludes most of the usual approaches.  We will begin by constructing the wave operators for spin-0 and spin-1/2 fields in these backgrounds and investigating the properties of solutions, analytically and numerically where necessary, on the simplest CHM – the Poincaré octagon in 2d.  We will attempt to generalize to more complex CHMs and to higher spin fields, and consider the implications to a variety of physical problems.