Relativistic GKLS master equation?

TL;DR

This paper examines the possibility of a relativistic generalization of the GKLS (Lindblad) master equation for open quantum systems, concluding that such Lorentz-invariant Markovian equations likely cannot exist due to fundamental issues.

Contribution

The paper critically analyzes the conjecture of a Lorentz-invariant GKLS master equation and demonstrates inherent defects preventing their existence.

Findings

Relativistic GKLS equations likely do not exist.

A hidden defect in the conjectured equations is identified.

The analysis challenges the feasibility of Lorentz-invariant Markovian quantum dynamics.

Abstract

The celebrated GKLS master equation, widely called just Lindblad equation, is the universal dynamical equation of non-relativistic open quantum systems in their Markovian approximation. It is not necessary and perhaps impossible that GKLS equations possess sensible relativistic forms. In a lucid talk on black hole information loss paradox, David Poulin conjectured a Lorentz invariant GKLS master equation. It remained unpublished. Poulin passed away at heights of his activity. But the equation is really puzzling. A closer look uncovers a smartly hidden defect which leaves us without Lorentz invariant Markovian master equations. They, in view of the present author, should not exist.