Nonlinear Dirac equations, Monotonicity Formulas and Liouville Theorems

TL;DR

This paper investigates nonlinear Dirac equations on Riemannian manifolds, deriving monotonicity formulas and Liouville theorems, and extends the analysis to Dirac-harmonic maps with curvature, contributing to mathematical physics and geometric analysis.

Contribution

It introduces new monotonicity formulas and Liouville theorems for nonlinear Dirac equations and extends these results to Dirac-harmonic maps with curvature.

Findings

Derived monotonicity formulas for nonlinear Dirac equations

Established Liouville theorems for solutions on Riemannian manifolds

Extended analysis to Dirac-harmonic maps with curvature

Abstract

We study the qualitative behavior of nonlinear Dirac equations arising in quantum field theory on complete Riemannian manifolds. In particular, we derive monotonicity formulas and Liouville theorems for solutions of these equations. Finally, we extend our analysis to Dirac-harmonic maps with curvature term.