Applications of metaplectic cohomology and global-local contact holonomy

Abstract

AbstractThe purpose of the paper is to elucidate by global-dual contact holonomy why one might expect the Foucault spherical pendulum’s spin echo-stabilized, symplectic swing-plane through the rotation axis of the spinning earth to follow a parallel vector field as time passes at a velocity depending on the latitude of the swivel’s location. The spinor geometric foundations of the paradigmatic Foucault spherical pendulum experiment of global-local contact holonomy exploit Hopf–Rinow type minimizing geodesic trajectories which appear as inertial traces designed by swing-planes on the terrestrial circular floor panel which is situated beneath the covariant motion of the oscillating pendulum device and where the linear traces are designing diameters of the spin structure induced Poincaré conformal hyperbolic open disc model. The quantum field theoretical evidence of the existence and uniqueness of categorizing parallel vector fields around smooth loops follows in terms of the open-book foliation with Hilbert space structures placed on the covariant pages.