Flux-Across-Surfaces Theorem for a Dirac Particle

Abstract

We consider the asymptotic evolution of a relativistic spin-1/2-particle. i.e. a particle whose wavefunction satisfies the Dirac equation with external static potential. We prove that the probability for the particle crossing a (detector) surface converges to the probability, that the direction of the momentum of the particle lies within the solid angle defined by the (detector) surface, as the distance of the surface goes to infinity. This generalizes earlier non relativistic results, known as flux across surfaces theorems, to the relativistic regime.

References in corpus (3)

• Scattering theory from microscopic first principles
• Zero-energy resonances and the flux -across-surfaces theorem
• The Flux-Across-Surfaces Theorem for a Point Interaction Hamiltonian

Cited by in corpus (8)

• A Relativistic Version of the Ghirardi-Rimini-Weber Model
• The Point Processes of the GRW Theory of Wave Function Collapse
• Adiabatic Pair Creation
• Born's Rule for Arbitrary Cauchy Surfaces
• Existence of Spontaneous Pair Creation
• A microscopic derivation of the quantum mechanical formal scattering cross section
• The Flux-Across-Surfaces Theorem under conditions on the scattering state
• Generalized Eigenfunctions for critical potentials with small perturbations