Quantum-Classical Interactions and Galois Type Extensions

Abstract

An algebraic model for the relation between a certain classical particle system and the quantum environment is proposed. The quantum environment is described by the category of possible quantum states. The initial particle system is represented by an associative algebra in the category of states. The key new observation is that particle interactions with the quantum environment can be described in terms of Hopf-Galois theory. This opens up a possibility to use quantum groups in our model of particle interactions.