TY - JOUR
TI - Scalar fields and spin-half fields on mildly singular spacetimes
DO - https://doi.org/doi:10.7282/T3ZP480H
PY - 2015
AB - A charged particle-spacetime is a solution to Einstein’s equations coupled to a nonlinear electromagnetic theory. It has a mild curvature singularity and a bounded electric potential. Morawetz and Strichartz estimates are proved for spherically symmetric scalar waves on such a spacetime. These spacetimes have conical singularities at their centers. As a first step towards understanding the behavior of scalar waves on such spacetimes, a way to reproduce the known fundamental solution to the scalar wave equation on flat two-dimensional cones is found using Sommerfeld’s method. Dirac’s equation for a spin-half field is set up on a charged particle-spacetime. The Dirac Hamiltonian is shown to be essentially self-adjoint on smooth functions with compact support away from the center. The essential spectrum and the continuous spectrum of the Hamiltonian are obtained. Under a certain condition, a neighbourhood of zero is shown to be in the resolvent. The existence of infinitely many eigenvalues is shown.
KW - Mathematics
KW - Scalar field theory
KW - Dirac equation
LA - eng
ER -