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

@article{Dappiaggi2018LinearizedFF, title={Linearized fields for causal variational principles: existence theory and causal structure}, author={Claudio Dappiaggi and Felix Finster}, journal={arXiv: Mathematical Physics}, year={2018} }

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… Expand

#### 11 Citations

Elliptic Methods for Solving the Linearized Field Equations of Causal Variational Principles

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A class of conserved surface layer integrals for causal variational principles

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In the theory of causal fermion systems, the physical equations are obtained as the Euler–Lagrange equations of a causal variational principle. Studying families of critical measures of causal… Expand

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The theory of causal fermion systems is a recent approach to fundamental physics. Giving quantum mechanics, general relativity and quantum field theory as limiting cases, it is a candidate for a… Expand

Fermionic Fock Spaces and Quantum States for Causal Fermion Systems

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It is shown for causal fermion systems describing Minkowski-type spacetimes that an interacting causal fermion system at time t gives rise to a distinguished state on the algebra generated by… Expand

A notion of entropy for causal fermion systems

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A notion of entropy is introduced for causal fermion systems. This entropy is a measure of the state of disorder of a causal fermion system at a given time compared to the vacuum. The definition is… Expand

Proposal 42: A New Storyline for the Universe Based on the Causal Fermion Systems Framework

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Based on preliminary results from the Causal Fermion Systems framework regarding the matter-antimatter asymmetry in the universe, I propose a novel story line for the universe that would, if correct,… Expand

Proposal 42.

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Based on preliminary results from the Causal Fermion Systems framework regarding the matter-antimatter asymmetry in the universe, I propose a novel story line for the universe that would, if correct,… Expand

Causal Fermion Systems: An Elementary Introduction to Physical Ideas and Mathematical Concepts

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We give an elementary introduction to the theory of causal fermion systems, with a focus on the underlying physical ideas and the conceptual and mathematical foundations.

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