Markovian quantum master equation with Poincar\'{e} symmetry

Abstract

We investigate what kind of Markovian quantum master equation (QME) in the Gorini-Kossakowski-Sudarshan-Lindblad (GKSL) form is realized under Poincar\'{e} symmetry. The solution of the Markovian QME is given by a quantum dynamical semigroup, for which we introduce invariance under Poincar\'{e} transformations. Using the invariance of the dynamical semigroup and applying the unitary representation of Poincar\'{e} group, we derive the Markovian QME for a relativistic massive spin-0 particle. Introducing the field operator of the massive particle and examining its evolution, we find that the field follows a dissipative Klein-Gordon equation. In addition, we show that any two local operators for spacelike separated regions commute with each other. This means that the microcausality condition is satisfied for the dissipative model of the massive particle.