The Homogeneous Causal Action Principle on a Compact Domain in Momentum Space

TL;DR

This paper introduces a homogeneous causal action principle on a compact momentum space domain, explores its connection to causal fermion systems, and analyzes the associated Euler-Lagrange equations.

Contribution

It presents a new formulation of the causal action principle in momentum space and investigates its mathematical properties and solutions.

Findings

Existence and compactness of solutions are established.

Euler-Lagrange equations are derived and analyzed.

Connections to causal fermion systems are clarified.

Abstract

The homogeneous causal action principle on a compact domain of momentum space is introduced. The connection to causal fermion systems is worked out. Existence and compactness results are reviewed. The Euler-Lagrange equations are derived and analyzed under suitable regularity assumptions.