Evolution integrals

Details Evolution integrals Evolution integrals

2006-02-02

arxiv.org/abs/math-ph/0602006v2

J. Operator Theory 60 (2008), 199--215.

Physics

Mathematical Physics

v1: 17 pages. v2: 19 pages, Section 3 extended, Section 4 shortened, Section 5 corrected

Scientific paper

A framework analogous to path integrals in quantum physics is set up for abstract dynamical systems in a W*-algebraic setting. We consider spaces of evolutions, defined in a specific way, of a W*-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.

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