Squares of White Noise, SL(2,C) and Kubo - Martin -Schwinger States

TL;DR

This paper explores the structure of KMS states on an algebra related to SL(2,C), establishing a correspondence with certain probability measures, and connects this to the square of white noise algebra.

Contribution

It identifies a one-to-one correspondence between covariant KMS states on an algebra extension of SL(2,C) and specific probability measures, linking to white noise algebra.

Findings

Existence of a one-to-one correspondence between KMS states and probability measures.

Characterization of KMS states via measures decreasing faster than any inverse polynomial.

Connection established between KMS states on algebra extension and square of white noise algebra.

Abstract

We investigate the structure of Kubo - Martin - Schwinger (KMS) states on some extension of the universal enveloping algebra of SL(2,C}. We find that there exists a one-to-one correspondence between the set of all covariant KMS states on this algebra and the set of all probability measures d\mu on the real half-line, which decrease faster than any inverse polynomial. This problem is connected to the problem of KMS states on square of white noise algebra.