Working directly with probabilities in quantum field theory

R Dickinson,J Forshaw,P Millington

doi:10.1088/1742-6596/880/1/012041

R Dickinson, J Forshaw + Show 1 more

Open Access

https://doi.org/10.1088/1742-6596/880/1/012041

Copy DOI

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.

Highlights

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
The utility of scattering-matrix theory has biased the development of techniques in quantum field theory towards the calculation of transition amplitudes
Atom A is initially prepared in an excited state, and atom B is initially prepared in its ground state

Summary

Introduction

The utility of scattering-matrix theory has biased the development of techniques in quantum field theory towards the calculation of transition amplitudes. 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. [10].) As we will see, this local measurement is independent of the state of atom A for all times T < R/c, being manifestly causal in the weak sense (see, e.g., Ref [11]).

Results

Conclusion