Dirac Kirchhoff diffraction theory

TL;DR

This paper derives Kirchhoff's scalar diffraction theory from the relativistic Dirac equation, highlighting fundamental similarities and extending the theory's applicability to electron and photon optics.

Contribution

It reformulates Kirchhoff's diffraction theory within the Dirac equation framework, bridging scalar and relativistic quantum descriptions.

Findings

Derivation of diffraction theory from Dirac equation

Highlighting parallels between scalar and relativistic wave equations

Basic interpretation of Fraunhofer diffraction in Dirac formalism

Abstract

Kirchhoff's scalar diffraction theory is applied throughout photon and electron optics. It is based on the stationary electromagnetic or Schr\"odinger wave equation, and is useful in describing interference phenomena for both light and matter waves. Here, Kirchhoff's diffraction theory is derived from the relativistic Dirac equation, thus reformulated to work on Dirac spinors. The parallels with the "classic" scalar theory are highlighted, and a basic interpretation of the result obtained for the Fraunhofer diffraction limit is given. The goal of this paper is to emphasize the similarity between the two equations on the most fundamental level.