Entangled Quantum States of Causal Fermion Systems and Unitary Group Integrals

TL;DR

This paper analyzes quantum states of causal fermion systems by computing asymptotic integrals over the unitary group, demonstrating the positivity of localized states and their capacity to describe entanglement.

Contribution

It provides a detailed asymptotic analysis of unitary group integrals, establishing conditions for positivity and entanglement in causal fermion systems.

Findings

Localized refined pre-states are positive in the limit.

The framework describes general entangled states.

Asymptotic integrals are computed for large dimensions.

Abstract

This paper is dedicated to a detailed analysis and computation of quantum states of causal fermion systems. The mathematical core is to compute integrals over the unitary group asymptotically for a large dimension of the group, for various integrands with a specific scaling behavior in this dimension. It is shown that, in a well-defined limiting case, the localized refined pre-state is positive and allows for the description of general entangled states.