Relativistic GKLS master equation?

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 It remained unpublished.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.

arXiv comment4pp, Fig. with explanation added

References in corpus (4)

• Dynamical Reduction Models
• Relativistic Collapse Model With Tachyonic Features
• Mass-coupled relativistic spontaneous collapse models
• Local Fields without Restrictions on the Spectrum of 4-Momentum Operator and Relativistic Lindblad Equation

Cited by in corpus (6)

• The classical-quantum hybrid canonical dynamics and its difficulties with special and general relativity
• Reduced dynamics with Poincaré symmetry in an open quantum system
• Classical-quantum scattering
• Decoherence-Free Entropic Gravity for Dirac Fermion
• Non-Hermitian Dirac theory from Lindbladian dynamics
• Spontaneous collapse effects on relativistic fermionic matter