# A Hamiltonian formulation of causal variational principles

@article{Finster2017AHF, title={A Hamiltonian formulation of causal variational principles}, author={Felix Finster and Johannes Kleiner}, journal={Calculus of Variations and Partial Differential Equations}, year={2017}, volume={56}, pages={1-33} }

Causal variational principles, which are the analytic core of the physical theory of causal fermion systems, are found to have an underlying Hamiltonian structure, giving a formulation of the dynamics in terms of physical fields in space-time. After generalizing causal variational principles to a class of lower semi-continuous Lagrangians on a smooth, possibly non-compact manifold, the corresponding Euler–Lagrange equations are derived. In the first part, it is shown under additional smoothness…

## 22 Citations

Dynamics of Causal Fermion Systems - Field Equations and Correction Terms for a New Unified Physical Theory

- Philosophy
- 2017

The theory of causal fermion systems is a new physical theory which aims to describe a fundamental level of physical reality. Its mathematical core is the causal action principle. In this thesis, we…

Elliptic methods for solving the linearized field equations of causal variational principles

- MathematicsCalculus of Variations and Partial Differential Equations
- 2022

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…

Complex structures on jet spaces and bosonic Fock space dynamics for causal variational principles

- Mathematics
- 2018

Based on conservation laws for surface layer integrals for minimizers of causal variational principles, it is shown how jet spaces can be endowed with an almost-complex structure. We analyze under…

Causal variational principles in the σ-locally compact setting: Existence of minimizers

- MathematicsAdvances in Calculus of Variations
- 2020

Abstract We prove the existence of minimizers of causal variational principles on second countable, locally compact Hausdorff spaces. Moreover, the corresponding Euler–Lagrange equations are derived.…

Causal variational principles in the infinite-dimensional setting: Existence of minimizers

- MathematicsAdvances in Calculus of Variations
- 2021

Abstract We provide a method for constructing (possibly non-trivial) measures on non-locally compact Polish subspaces of infinite-dimensional separable Banach spaces which, under suitable…

Banach manifold structure and infinite-dimensional analysis for causal fermion systems

- MathematicsAnnals of Global Analysis and Geometry
- 2021

A mathematical framework is developed for the analysis of causal fermion systems in the infinite-dimensional setting. It is shown that the regular spacetime point operators form a Banach manifold…

Causal Fermion Systems: Discrete Space-Times, Causation and Finite Propagation Speed

- Physics, PhilosophyJournal of Physics: Conference Series
- 2019

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…

H\"older Continuity of the Integrated Causal Lagrangian in Minkowski Space

- Physics
- 2021

It is proven that the kernel of the fermionic projector of regularized Dirac sea vacua in Minkowski Space is L-integrable. The proof is carried out in the specific setting of a continuous…

Perturbation theory for critical points of causal variational principles

- Mathematics
- 2017

The perturbation theory for critical points of causal variational principles is developed. We first analyze the class of perturbations obtained by multiplying the universal measure by a weight…

Positive Functionals Induced by Minimizers of Causal Variational Principles

- Mathematics
- 2017

Considering second variations about a given minimizer of a causal variational principle, we derive positive functionals in space-time. It is shown that the strict positivity of these functionals…

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