Nonlinear conformal-degree preserving Dirac equations

TL;DR

This paper derives nonlinear Dirac equations with conformal degree preservation in various dimensions, highlighting their connection to known models like Thirring and Gross-Neveu, and provides numerical solutions for specific symmetric modes.

Contribution

It introduces a class of nonlinear Dirac equations with conformal invariance and explores their relation to established models, including numerical analysis.

Findings

Derivation of conformal-degree preserving nonlinear Dirac equations.

Identification of these equations with known models like Thirring and Gross-Neveu.

Numerical solutions for spin and pseudo-spin symmetric modes.

Abstract

Nonlinear Dirac equations in D+1 space-time are obtained by variation of the spinor action whose Lagrangian components have the same conformal degree and the coupling parameter of the self-interaction term is dimensionless. In 1+1 dimension, we show that these requirements result in the "conventional" quartic form of the nonlinear interaction and present the general equation for various coupling modes. These include, but not limited to, the Thirring and Gross-Neveu models. We obtain a numerical solution for the special case of the spin and pseudo-spin symmetric modes..