A Note on the Relativistic Transformation Properties of Quantum Stochastic Calculus

Abstract

We give a simple argument to derive the transformation of quantum stochastic calculus formalism between inertial observers, and derive the quantum open system dynamics for a system moving in a vacuum (more generally coherent) quantum field under the usual Markov approximation. We argue that for uniformly accelerated open systems, however, the formalism must breakdown as we move from a Fock representation over the algebra of field observables over all Minkowski space to the restriction to the algebra of observables over a Rindler wedge. This leads to quantum noise having a unitarily inequivalent non-Fock representation - in particular, the latter is a thermal representation at the Unruh temperature. The unitary inequivalence ultimately being a consequence of the underlying flat noise spectrum approximation for the fundamental quantum stochastic processes. We derive the quantum stochastic limit for a uniformly accelerated (two-level) detector and establish an open systems description of the relaxation to thermal equilibrium at the Unruh temperature.er is a thermal representation at the Unruh temperature. The unitary inequivalence ultimately being a consequence of the underlying flat noise spectrum approximation for the fundamental quantum stochastic processes.