Detection Time Distribution for Dirac Particles

TL;DR

This paper develops a relativistic detection time distribution rule for Dirac particles using an absorbing boundary condition, applicable in various space-time geometries and detector configurations.

Contribution

It introduces a relativistic extension of the absorbing boundary rule for Dirac particles, broadening its applicability to curved space-time and moving detectors.

Findings

Formulated a relativistic boundary condition for Dirac particles.

Applied the rule to flat and curved space-time scenarios.

Supported the rule's consistency with relativistic quantum mechanics.

Abstract

The problem of detection time distribution concerns a quantum particle surrounded by detectors and consists of computing the probability distribution of where and when the particle will be detected. While the correct answer can be obtained in principle by solving the Schrodinger equation of particle and detectors together, a more practical answer should involve a simple rule representing the behavior of idealized detectors. We have argued elsewhere [http://arxiv.org/abs/1601.03715] that the most natural rule for this purpose is the "absorbing boundary rule," based on the 1-particle Schrodinger equation with a certain "absorbing" boundary condition, first considered by Werner in 1987, at the ideal detecting surface. Here we develop a relativistic variant of this rule using the Dirac equation and also a boundary condition. We treat one or several detectable particles, in flat or curved space-time, with stationary or moving detectors.