Symmetric states for $C^*$-Fermi systems I: De Finetti theorem

TL;DR

This paper extends the De Finetti theorem to infinite Fermi $C^*$-tensor products, providing a foundational understanding of symmetric states in Fermi systems within operator algebra frameworks.

Contribution

It introduces a novel extension of the De Finetti theorem specifically for infinite Fermi $C^*$-tensor products of graded $C^*$-algebras, advancing the mathematical theory of Fermi systems.

Findings

Extension of De Finetti theorem to Fermi $C^*$-systems

Characterization of symmetric states in infinite Fermi tensor products

Foundational framework for future studies in Fermi quantum systems

Abstract

n the present note, which is the first part of a work concerning the study of the set of the symmetric states for Fermi systems, we describe the extension of the De Finetti theorem to the infinite Fermi $C^*$-tensor product of a single (separable) general $\bz^2$-graded $C^*$-algebra.