Probabilities and signalling in quantum field theory

Abstract

We present an approach to computing probabilities in quantum field theory for a wide class of source-detector models. The approach works directly with probabilities and not with squared matrix elements, and the resulting probabilities can be written in terms of expectation values of nested commutators and anti-commutators. We present results that help in the evaluation of these, including an expression for the vacuum expectation values of general nestings of commutators and anti-commutators in scalar field theory. This approach allows one to see clearly how faster-than-light signalling is prevented, because it leads to a diagrammatic expansion in which the retarded propagator plays a prominent role. We illustrate the formalism using the simple case of the much-studied Fermi two-atom problem.

arXiv comment23 pages, 3 figures; to match published version

References in corpus (8)

• There are No Causality Problems for Fermi's Two Atom System
• Causality issues of particle detector models in QFT and Quantum Optics
• Instantaneous Spreading and Einstein Causality in Quantum Theory
• The relativistic quantum channel of communication through field quanta
• Renormalized Unruh-DeWitt Particle Detector Models for Boson and Fermion Fields
• Perturbation theory for quantum-mechanical observables
• Manifest causality in quantum field theory with sources and detectors
• The limits of the rotating wave approximation in the electromagnetic field propagation in a cavity

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• The Fermi problem in disordered systems
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• A new study of the Unruh effect
• Fock-space projection operators for semi-inclusive final states
• Relating quantum mechanics and kinetics of neutrino oscillations
• Fermi two-atom problem: non-perturbative approach via relativistic quantum information and algebraic quantum field theory