agnetic field for charged particles, while particles react back onto the fields being sources for the latter, for instance through the charge and current density sources of the electromagnetic field in Maxwell’s equations (the same characterisation applies to the gravitational field equations of general relativity). This dichotomic distinction between matter and radiation is unified in a dual form when considering a relativistic quantum framework. Indeed, it then turns out that particles are nothing else than the quanta, [*i.e.*]{}, the quantum states of definite energy, momentum and spin, of quantum fields. Particles and fields are just the two complementary aspects of the quantum relativistic world of point-particles. All electrons, for example, are identical, being quanta of a single electron field filling all of spacetime. To each distinct species of particle corresponds a field, and vice-versa. This, in a word, is the essence of quantum field theory: the natural framework for a description of relativistic quantum point-particles, explaining their corpuscular properties when detected in energy-momentum eigenstates and their wave behaviour when considering their spacetime propagation. Let us briefly express these points in a somewhat more mathematical setting.

Particles and Fields {#Sec2.1}
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A free relativistic field may be seen to correspond to an infinite collection of harmonic oscillators sitting at each point in space, and coupled to one another through a nearest-neighbour term in the action of the field’s dynamics. Let us first recall a few basic facts about the one-dimensional harmonic oscillator. Its dynamics derives through the variational principle from the action $$S[q]=\int dt\,m\left[\frac{1}{2}\left(\frac{dq}{dt}\right)^2-
\frac{1}{2}\omega^2q^2\right]\ ,
\label{eq:SHO}$$ where $q(t)\in\mathbb R$ is the configuration space of the system. How to perform the standard canonical operator quantisation of this system is well known,[@GovCOPRO2] leading, in the Heisenberg picture