Causal fermion systems and the ETH approach to quantum theory

Felix Finster; Jürg Fröhlich; Marco Oppio; Claudio F. Paganini

doi:10.3934/dcdss.2020451

Article Contents

2021, Volume 14, Issue 5: 1717-1746. Doi: 10.3934/dcdss.2020451

This issue Previous Article A survey on asymptotic stability of ground states of nonlinear Schrödinger equations II Next Article On a class of semipositone problems with singular Trudinger-Moser nonlinearities

Causal fermion systems and the ETH approach to quantum theory

1.
Fakultät für Mathematik, Universität Regensburg, D-93040 Regensburg, Germany
2.
Institute of Theoretical Physics, ETH Zurich, Switzerland
3.
Fakultät für Mathematik, Universität Regensburg, D-93040 Regensburg, Germany
4.
Max Planck Institute for Gravitational Physics (Albert Einstein Institute), Am Mühlenberg 1, D-14476 Potsdam, Germany

^* Corresponding author: Felix Finster
^* Corresponding author: Felix Finster

Received: April 2020

Revised: August 2020

Early access: November 2020

Published: May 2021

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Abstract

After reviewing the theory of "causal fermion systems" (CFS theory) and the "Events, Trees, and Histories Approach" to quantum theory (ETH approach), we compare some of the mathematical structures underlying these two general frameworks and discuss similarities and differences. For causal fermion systems, we introduce future algebras based on causal relations inherent to a causal fermion system. These algebras are analogous to the algebras previously introduced in the ETH approach. We then show that the spacetime points of a causal fermion system have properties similar to those of "events", as defined in the ETH approach. Our discussion is underpinned by a survey of results on causal fermion systems describing Minkowski space that show that an operator representing a spacetime point commutes with the algebra in its causal future, up to tiny corrections that depend on a regularization length.

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Mathematics Subject Classification: 83A05, 81T05, 81P15, 47N50, 81R15, 49S05.

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Figure 1. The spacetime restricted causal future $ I^\vee_\rho(x) $ of the causal fermion system and the future light cone $ \mathcal{I}^\vee(x) $ of Minkowski space

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Figure 2. The approximate center and the loss of access to information

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