SQUARES OF WHITE NOISE, SL(2, ℂ) AND KUBO–MARTIN–SCHWINGER STATES

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 dμ on the real half-line [0, +∞), which decrease faster than any inverse polynomial. This problem is connected to the problem of KMS states on square of white noise algebra.