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Mathematical Physics, math-ph,Mathematics, Mathematical Physics, math.MP,Quantum Physics, quant-ph
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.
