Geometry of Quasi-Free States of CCR Algebras

TL;DR

This paper explores the geometric structure of square roots of quasi-free states in CCR algebras and provides an explicit formula for calculating transition amplitudes between these states.

Contribution

It introduces a geometric perspective on quasi-free states and derives a new explicit formula for transition amplitudes among them.

Findings

Geometric characterization of square roots of quasi-free states.

Explicit formula for transition amplitudes.

Enhanced understanding of state transitions in CCR algebras.

Abstract

Geometric positions of square roots of quasi-free states of CCR algebras are investigated together with an explicit formula for transition amplitudes among them.