The study of the interactions between electrically charged particles and electromagnetic fields within the framework of QFT is called quantum electrodynamics (QED). QED, and in particular its renormalized perturbative formulation, was modeled by various theories to describe other interactions, and thus became the starting point for a new research programme, the quantum field programme (QFP). The programme has been implemented by a series of theories, whose developments are strongly constrained by some of its characteristic features, which have been inherited from QED. For this reason, I shall start this review of the sinuous evolution of QFP with an outline of these features.

Essential features

QED is a theoretical system consisting of local field operators that obey equations of motion, certain canonical commutation and anticommutation relations (for bosons and fermions, respectively), and a Hilbert space of state vectors that is obtained by the successive application of the field operators to the vacuum state, which, as a Lorentz invariant state devoid of any physical properties, is assumed to be unique. Let us look in greater detail at three assumptions that underlie the system.

First is the locality assumption. According to Dirac (1948), ‘a local dynamical variable is a quantity which describes physical conditions at one point of space-time. Examples are field quantities and derivatives of field quantities,’ and “a dynamical system in quantum theory will be defined as localizable if a representation for the wave function can be set up in which all the dynamical variables are localizable’.