Causal Fermion Systems and the ETH Approach to Quantum Theory

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.

arXiv comment31 pages, LaTeX, 2 figures, minor improvements (published version)

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Cited by in corpus (3)

• A Mechanism of Baryogenesis for Causal Fermion Systems
• Modified Measures as an Effective Theory for Causal Fermion Systems
• Local Algebras for Causal Fermion Systems in Minkowski Space