An integrodifferential Dirac equation with quantized charge in one space dimension
The author proposes a one-dimensional integrodifferential Dirac equation: \[ i\gamma^{\mu} \partial_{\mu} \psi -(m^ 2/\lambda)\sin \{4\lambda \int^{P}_{Q}{\bar \psi} i \gamma_{\mu} \gamma^ 5 \psi dx^{\mu}\}B\psi =0, \] which has solitonic solutions, quantized charge and positive definite energy density. This is claimed as a spinorial version of the sine-Gordon equation and hence termed as sine-Dirac equation. With mass m/\(\lambda\), charge \(\pi\) /2\(\lambda\), which are the same as those of the Thirring soliton with \(\delta =\pi /2\), the study of the model leads to quite interesting results on the direct coupling of an extended particle essentially consisting of confined constituents.
scientific article; zbMATH DE number 3935712