Galilean covariance of quantum-classical hybrid systems of the Sudarshan type

TL;DR

This paper examines the Galilean covariance of Sudarshan-type quantum-classical hybrid systems, revealing that such systems cannot be both Galilean covariant and momentum-conserving unless their interaction depends solely on relative velocities.

Contribution

It demonstrates the incompatibility of Galilean covariance with certain hybrid quantum-classical systems and specifies conditions for momentum conservation.

Findings

Hybrid systems cannot be a unitary Galilei group representation.

Momentum conservation requires interaction dependence on relative velocities.

Galilean covariance imposes constraints on hybrid system interactions.

Abstract

We revisit quantum-classical hybrid systems of the Sudarshan type under the light of Galilean covariance. We show that these kind of hybrids cannot be given as a unitary representation of the Galilei group and at the same time conserve the total linear momentum unless the interaction term only depends on the relative canonical velocities.