Methods and Applications of Analysis

Volume 27 (2020)

Number 1

Linearized fields for causal variational principles: existence theory and causal structure

Pages: 1 – 56



Claudio Dappiaggi (Dipartimento di Fisica, Università degli Studi di Pavia, Italy; and INFN, Sezione di Pavia, Italy)

Felix Finster (Fakultät für Mathematik, Universität Regensburg, Germany)


The existence theory for solutions of the linearized field equations for causal variational principles is developed. We begin by studying the Cauchy problem locally in lens-shaped regions, defined as subsets of space-time which admit foliations by surface layers satisfying hyperbolicity conditions. We prove existence of weak solutions and show uniqueness up to vectors in the orthogonal complement of the jets used for testing. The connection between weak and strong solutions is analyzed. Global solutions are constructed by exhausting space-time by lens-shaped regions. We construct advanced and retarded Green’s operators and study their properties.


causal variational principles, existence theory of solutions, Green’s operators

2010 Mathematics Subject Classification

35Axx, 35B38, 49Q20, 49S05

Received 2 December 2018

Accepted 15 November 2019

Published 12 August 2020