The affine property of quasi-free states on self-dual CAR algebras

TL;DR

This paper investigates the conditions under which the relationship between quasi-free states on self-dual CAR algebras and covariant operators is affine, enhancing understanding of their mathematical structure.

Contribution

It identifies specific conditions that ensure the affine correspondence between quasi-free states and covariant operators on self-dual CAR algebras.

Findings

Established criteria for affinity in the state-operator correspondence

Clarified the mathematical structure of quasi-free states

Provided insights into the algebraic properties of self-dual CAR algebras

Abstract

We study conditions for which the correspondence between quasi-free states on self-dual CAR algebras and covariant operators is affine.