Particle geodesics and spectra in the spacetime tangent bundle

A limiting curvature of worldlines in spacetime serves as a possible basis for the differential geometry of the tangent bundle of spacetime. I first review briefly the resulting differential geometric structure of the spacetime tangent bundle. Next, I examine the relations between bundle geodesies and their projections on the spacetime base manifold. Possible classical particle equations of motion result from geodesic motion in the bundle manifold. Additionally, the Laplace-Beltrami operator is constructed on the bundle manifold. Possible particle spectra are represented by quantum fields that have a null eigenvalue when acted upon by the Laplace-Beltrami operator of the bundle manifold. The fields are shown to be automatically regularized by the limiting curvature of worldlines in spacetime, and particle spectra are shown to be cut off at very high energy.