Working directly with probabilities in quantum field theory

Abstract

We present a novel approach to computing transition probabilities in quantum field theory, which allows them to be written directly in terms of expectation values of nested commutators and anti-commutators of field operators, rather than squared matrix elements. We show that this leads to a diagrammatic expansion in which the retarded propagator plays a dominant role. As a result, one is able to see clearly how faster-than-light signalling is prevented between sources and detectors. Finally, we comment on potential implications of this approach for dealing with infra-red divergences.

Comments: 8 pages, 2 figures. Prepared for the proceedings of the 8th International Workshop DICE2016 Spacetime - Matter - Quantum Mechanics, 12-16 September 2016, Castiglioncello, Italy, to appear in the Journal of Physics: Conference Series (JPCS). Presented by P. Millington