# Energy methods for Dirac-type equations in two-dimensional Minkowski space

## TL;DR

This paper develops energy methods to analyze a broad class of Dirac-type equations in two-dimensional Minkowski space, establishing existence results for equations relevant in quantum field theory, including Dirac-wave maps.

## Contribution

It introduces new energy techniques for Dirac equations in 2D Minkowski space and proves existence results for equations from quantum field theory.

## Key findings

- Established existence results for Dirac-wave maps.
- Developed energy methods applicable to nonlinear Dirac equations.
- Extended analysis to equations with geometric and physical significance.

## Abstract

In this article we develop energy methods for a large class of linear and nonlinear Dirac-type equations in two-dimensional Minkowski space. We will derive existence results for several Dirac-type equations originating in quantum field theory, in particular for Dirac-wave maps to compact Riemannian manifolds.