Quantum field theory of single-photon states

Abstract We present a detailed quantum field theory of single-photon states. The formalism we develop permits us to calculate the electric field of a single-photon light beam sent through a beam splitter (BS). This illustrates the nonlocal nature of quantum fields even when they are excited by discrete numbers of quanta. We find that the shape of the electromagnetic wave attached to a single photon entering the BS, determines the results of simultaneous measurements at two different locations behind the two ports of the BS. Therefore, our results confirm that a quantum field can be both local with respect to its discrete excitations, i.e. the photons, and nonlocal with respect to its continuous amplitude.