Construction of Global Solutions to the Linearized Field Equations for Causal Variational Principles

TL;DR

This paper introduces a new method for constructing global solutions to linearized field equations in causal variational principles by gluing local solutions, and explores applications like Green's operators and cone structures.

Contribution

It presents a novel approach to build global solutions from local ones in the context of causal variational principles, advancing the mathematical framework.

Findings

Construction of causal Green's operators

Introduction of cone structures in the solution space

Validation of the gluing method for local solutions

Abstract

We give a novel construction of global solutions to the linearized field equations for causal variational principles. The method is to glue together local solutions supported in lens-shaped regions. As applications, causal Green's operators and cone structures are introduced.