Dynamical Maps and Symmetroids
Abstract
Starting from the canonical symmetroid associated with a groupoid , the issue of describing dynamical maps in the groupoidal approach to quantum mechanics is addressed. After inducing a Haar measure on the canonical symmetroid , the associated von Neumann groupoid algebra is constructed. It is shown that the left-regular representation allows to define linear maps on the groupoid-algebra of the groupoid and given subsets of functions are associated with completely positive maps. Some simple examples are also presented.