The Analytic Quantum Information Manifold

by R. F. Streater. Published in the Albeverio Festschrift, a volume to celebrate the 60 birthday of Sergio Albeverio; entitled "Stochastic Processes, Physics and Geometry; new interplays", the book is edited by Sylvie Paycha, Fritz Gesztesy and Helge Holden, and published as: Canadian Math. Soc. Conf. Proc. 29, 603-611, 2000.

ABSTRACT

Let H &geq I be a self-adjoint operator on a Hilbert space, such that exp(-beta H) is of trace-class for some beta less than 1. Let V be a symmetric operator such that ||V||_\omega:=||RV|| is finite, where R=H^{-1}. We show that the partition function Tr exp-(H+V) is analytic in lambda in a hood of the origin, in the sense of Fréchet, in the Banach space with norm || . ||_\omega. This is used to supply the quantum information manifold defined by H with a real-analytic structure.

The text is available on the archives math-ph/9910036.