Time-of-arrival formalism for the relativistic particle
Abstract
Description
A suitable operator for the time-of-arrival at a detector is defined for the free relativistic particle in 3+1 dimensions. For each detector position, there exists a subspace of detected states in the Hilbert space of solutions to the Klein Gordon equation. Orthogonality and completeness of the eigenfunctions of the time-of-arrival operator apply inside this subspace, opening up a standard probabilistic interpretation.
16 pages, no figures, uses LaTeX. The section "Interpretation" has been completely rewritten and some errors corrected
16 pages, no figures, uses LaTeX. The section "Interpretation" has been completely rewritten and some errors corrected