Generalized solutions and distributional shadows for Dirac equations

TL;DR

This paper explores generalized solutions and distributional limits for Dirac equations, providing explicit forms for free fields with point-like initial data, advancing mathematical understanding of quantum field behavior.

Contribution

It introduces new methods for analyzing distributional limits of Dirac equations, extending previous results to include explicit forms for free fields with point-like initial conditions.

Findings

Derived explicit distributional forms for free Dirac fields.

Established existence of distributional limits for regularized initial data.

Extended mathematical framework for Dirac equations with external fields.

Abstract

We discuss the application of recent results on generalized solutions to the Cauchy problem for hyperbolic systems to Dirac equations with external fields. In further analysis we focus on the question of existence of associated distributional limits and derive their explicit form in case of free Dirac fields with regularizations of initial values corresponding to point-like probability densities.