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.\u00a0 In order to understand the detailed phenomenological implications of these compact hyperbolic manifolds (CHMs) for phenomena as varied as super-symmetry breaking and\u00a0 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.\u00a0 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 Poincar\u00e9 octagon in 2d.\u00a0 We will attempt to generalize to more complex CHMs and to higher spin fields, and consider the implications to a variety of physical problems.<\/span><\/p>\n","protected":false},"excerpt":{"rendered":" Chad Davis with \u00a0Glenn StarkmanHigher Spin Wave Equations on Compact Hyperbolic Manifolds and Applications<\/p>\n 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.\u00a0 In order to understand the detailed phenomenological implications of these compact hyperbolic manifolds (CHMs) for phenomena as varied as super-symmetry breaking and\u00a0 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.<\/p>\n