Modular Conjugation and the Implementation of Supersymmetry

TL;DR

This paper develops a framework for representing Z_2-graded C*-dynamical systems with graded-KMS functionals using modular conjugation, extending to unbounded functionals with dense domain unions.

Contribution

It introduces a canonical representation of graded C*-systems with graded-KMS functionals via modular conjugation, including unbounded cases with dense domain unions.

Findings

Representation as Z_2-graded operator algebras using modular conjugation

Extension to unbounded graded-KMS functionals with dense domains

Proving the modulus of unbounded graded-KMS functional is KMS

Abstract

Any Z_2-graded C*-dynamical system with a self-adjoint graded-KMS functional on it can be represented (canonically) as a Z_2-graded algebra of bounded operators on a Z_2-graded Hilbert space, so that the grading of the latter is compatible with the functional. The modular conjugation operator plays a crucial role in this reconstruction. The results are generalized to the case of an unbounded graded-KMS functional having as dense domain the union of a net of C*-subalgebras. It is shown that the modulus of such an unbounded graded-KMS functional is KMS.