# Journal of Operator Theory

Volume 60, Issue 1, Summer 2008 pp. 199-215.

Evolution integrals**Authors**: Rocco Duvenhage

**Author institution:**Department of Mathematics and Applied Mathematics, University of Pretoria, Pretoria, 0002, South Africa

**Summary:**A framework analogous to path integrals in quantum physics is set up for dynamical systems in a $W^{\ast}$-algebraic setting. We consider spaces of evolutions, defined in a specific way, of a $W^{\ast}% $-algebra $A$ as an analogue of spaces of classical paths, and show how integrals over such spaces, which we call ``evolution integrals'', lead to dynamics in a Hilbert space on a ``higher level'' which is viewed as an analogue of quantum dynamics obtained from path integrals. The measures with respect to which these integrals are performed are projection valued.

Contents Full-Text PDF