Non-locality and causal evolution in QFT

Non-locality appearing in QFT during the free evolution of localized field states and in the Feynman propagator function is analysed. It is shown to be connected to the initial non-local properties present at the level of quantum states and it does not imply a violation of Einstein's causality. Then a simple QFT system with interaction, consisting of a classical source coupled linearly to a quantum scalar field is investigated and is exactly solved. The expression for the time evolution of the state describing the system is given. The expectation value of any arbitrary 'good' local observable, expressed as a function of the field operator and its space and time derivatives, is obtained explicitly at all orders in the field-matter coupling constant. These expectation values have a source-dependent part that is shown to be always causally retarded, while the non-local contributions are source independent and related to the non- local properties of zero-point vacuum fluctuations.