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

Finster, Felix; Jokel, Maximilian

doi:10.48550/arxiv.1908.08451

Cited by 14 publications

(22 citation statements)

References 23 publications

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“…The theory of causal fermion systems is a recent approach to fundamental physics (see the reviews [17,14,13], the textbook [12] or the website [1]). In this approach, spacetime and all objects therein are described by a measure ρ on a set F of linear operators of a Hilbert space (H, .|.…”

Section: Introductionmentioning

confidence: 99%

Numerical Analysis of the Causal Action Principle in Low Dimensions

Finster¹,

Jonsson²,

Kilbertus³

2022

Preprint

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The numerical analysis of causal fermion systems is advanced by employing differentiable programming methods. The causal action principle for weighted counting measures is introduced for general values of the integer parameters f (the particle number), n (the spin dimension) and m (the number of spacetime points). In the case n = 1, the causal relations are clarified geometrically in terms of causal cones. Discrete Dirac spheres are introduced as candidates for minimizers for large m in the cases n = 1, f = 2 and n = 2, f = 4. We provide a thorough numerical analysis of the causal action principle for weighted counting measures for large m in the cases n = 1, 2 and f = 2, 3, 4. Our numerical findings corroborate that all minimizers for large m are good approximations of the discrete Dirac spheres. In the example n = 1, f = 3 it is explained how numerical minimizers can be visualized by projected spacetime plots. Methods and prospects are discussed to numerically investigate settings in which hitherto no analytic candidates for minimizers are known.

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Section: Introductionmentioning

confidence: 99%

Numerical Analysis of the Causal Action Principle in Low Dimensions

Finster¹,

Jonsson²,

Kilbertus³

2022

Preprint

Self Cite

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“…The theory of causal fermion systems is a recent approach to fundamental physics (see the basics in Section 2, the reviews [13,15,21], the textbook [12] or the website [1]). In this approach, spacetime and all objects therein are described by a measure ρ on a set F of linear operator of a Hilbert space (H, .|.…”

Section: Introductionmentioning

confidence: 99%

Fermionic Fock Spaces and Quantum States for Causal Fermion Systems

Finster,

Kamran

2021

Preprint

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“…The theory of causal fermion systems is a novel approach to fundamental physics (see the reviews [14,9,6], the textbook [4] or the website [1]). Recently, the connection to quantum states has been ciao established [10,11].…”

Section: Introductionmentioning

confidence: 99%

Linear Bosonic Quantum Field Theories Arising from Causal Variational Principles

Dappiaggi,

Finster,

Oppio

2021

Preprint

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

Abstract: 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.

Cited by 14 publications

References 23 publications

Numerical Analysis of the Causal Action Principle in Low Dimensions

Numerical Analysis of the Causal Action Principle in Low Dimensions

Fermionic Fock Spaces and Quantum States for Causal Fermion Systems

Linear Bosonic Quantum Field Theories Arising from Causal Variational Principles

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