Fermionic Fock Spaces and Quantum States for Causal Fermion Systems

TL;DR

This paper demonstrates how interacting causal fermion systems in Minkowski spacetime naturally define positive quantum states on associated field operator algebras, with explicit constructions and proofs of positivity.

Contribution

It introduces a method to derive quantum states from interacting causal fermion systems, establishing positivity and constructing representations.

Findings

States are derived from causal fermion systems in Minkowski spacetime.

Positivity of the constructed states is proven.

Explicit representations of the states are constructed.

Abstract

It is shown for causal fermion systems describing Minkowski-type spacetimes that an interacting causal fermion system at time $t$ gives rise to a distinguished state on the algebra generated by fermionic and bosonic field operators. The proof of positivity of the state is given and representations are constructed.