Transparent Dirac potentials in one dimension: the time-dependent case

TL;DR

This paper extends the class of transparent Dirac potentials to include time-dependent cases in one dimension, unifying known solutions and aiding semi-classical analysis of certain quantum field theories.

Contribution

It generalizes static transparent potentials to time-dependent ones, encompassing all known solutions and facilitating applications in fermionic quantum field theories.

Findings

Includes all known transparent potentials as special cases

Provides a framework for time-dependent solutions in Dirac equations

Aids semi-classical analysis of 1+1 dimensional fermionic theories

Abstract

We generalize the original derivation of transparent, static Schroedinger potentials by Kay and Moses, to obtain a large class of time-dependent transparent Dirac potentials in one spatial dimension. They contain all known transparent potentials as special cases and play a key role in the semi-classical solution of 1+1 dimensional, fermionic quantum field theories of Gross-Neveu and Nambu-Jona-Lasinio type.