# 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…

## 12 Citations

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

- Physics, Mathematics
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The existence theory is developed for solutions of the inhomogeneous linearized field equations for causal variational principles. These equations are formulated weakly with an integral operator…

A class of conserved surface layer integrals for causal variational principles

- Mathematics, PhysicsCalculus of Variations and Partial Differential Equations
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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…

The linear dynamics of wave functions in causal fermion systems

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- 2021

The dynamics of spinorial wave functions in a causal fermion system is studied. A so-called dynamical wave equation is derived. Its solutions form a Hilbert space, whose scalar product is represented…

A Positive Mass Theorem for Causal Fermion Systems

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- 2019

Asymptotically flat static causal fermion systems are introduced. Their total mass is defined as a limit of surface layer integrals which compare the measures describing the asymptotically flat…

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- Physics, MathematicsJournal of Physics: Conference Series
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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…

Linear Bosonic Quantum Field Theories Arising from Causal Variational Principles

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It is shown that the linearized fields of causal variational principles give rise to linear bosonic quantum field theories. The properties of these field theories are studied and compared with the…

Fermionic Fock Spaces and Quantum States for Causal Fermion Systems

- Physics, MathematicsAnnales Henri Poincaré
- 2021

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…

A notion of entropy for causal fermion systems

- Physics, MathematicsLetters in Mathematical Physics
- 2021

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…

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

- Physics
- 2018

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,…

Proposal 42.

- Physics
- 2018

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,…

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