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Zeitschrift für Analysis und ihre Anwendungen


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Volume 11, Issue 4, 1992, pp. 455–488
DOI: 10.4171/ZAA/590

Published online: 1992-12-31

A Study on the Geometry of Pairs of Positive Linear Forms, Algebraic Transition Probability and Geometrical Phase over Non-Commutative Operator Algebras (II)

Peter M. Alberti[1]

(1) Universität Leipzig, Germany

The results of the first part [1] will be used to discuss and to investigate some extensions of geometrical notions, which recently have been found to be of interest in Mathematical Physics in context of the problems of the so-called geometrical phase. The concepts of the global phase, the phase group and holonomy group of a normal state of a $vN$-algebra will be introduced and discussed.

Keywords: Functional analysis, $C*$-algebras, $vN$-algebras, non-commutative probability, non-commutative geometry

Alberti Peter: A Study on the Geometry of Pairs of Positive Linear Forms, Algebraic Transition Probability and Geometrical Phase over Non-Commutative Operator Algebras (II). Z. Anal. Anwend. 11 (1992), 455-488. doi: 10.4171/ZAA/590