Reduced dynamics with Poincaré symmetry in an open quantum system

Abstract

We consider how the reduced dynamics of an open quantum system coupled to an environment admits the Poincaré symmetry. The reduced dynamics is described by a dynamical map, which is given by tracing out the environment from the total unitary evolution without initial correlations. We investigate the dynamical map which is invariant under the Poincaré group. Based on the unitary representation theory of the Poincaré group, we develop a systematic way to give such a dynamical map. Using this way, we derive the dynamical map of a massive particle with a finite spin and a massless particle with a finite spin and a nonzero momentum. The dynamical map of a spinless massive particle is exemplified and the conservation of the Poincaré generators is discussed. We then find the map with the Poincaré invariance and the four-momentum conservation. Further, we show that the conservation of the angular momentum and the boost operator makes the map of a spinless massive particle unitary

31 pages, 1 table

References in corpus (7)

• Extending Noether's theorem by quantifying the asymmetry of quantum states
• A Relativistic Dynamical Collapse Model
• Mass-coupled relativistic spontaneous collapse models
• Asymptotic measurement schemes for every observable of a quantum field theory
• Relativistic GKLS master equation?
• Relativistic quantum field theory of stochastic dynamics in the Hilbert space
• Double-trace deformation in Keldysh field theory

Cited by in corpus (4)

• The Open Effective Field Theory of Inflation
• Classical-quantum scattering
• Non-Hermitian Dirac theory from Lindbladian dynamics
• Spontaneous collapse effects on relativistic fermionic matter