Dynamics-generating semigroups and phenomenology of decoherence

TL;DR

This paper reviews and extends the Dynamics-Generating Approach (DGA), demonstrating how it derives quantum dynamics, path integrals, and decoherence phenomena from semigroup structures related to Galilei symmetry.

Contribution

It introduces a generalized DGA framework that derives path integrals and decoherence dynamics from semigroup structures, without relying on postulated measures.

Findings

Derivation of Feynman path integrals from semigroup structures.

Phenomenological description of decoherence and dissipation.

Extension of DGA to open quantum systems.

Abstract

The earlier proposed Dynamics-Generating Approach (DGA) is reviewed and extended. Starting from an arbitrarily chosen group or semigroup which have structure similar to the structure of Galilei group, DGA allows one to construct phenomenological description of dynamics of the corresponding "elementary quantum object" (a particle or non-local object of special type). A class of Galilei-type semigroups, with semigroup of trajectories (parametrized paths) instead of translations, allows one to derive Feynman path integrals in the framework of DGA. The measure of path integrating (exponential of the classic action) is not postulated but derived from the structure of projective semigroup representations. The generalization of DGA suggested in the present paper allows one to derive dynamics of open quantum systems. Specifically, phenomenological description of decoherence and dissipation of a non-relativistic particle is derived from Galilei semigroup.