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Electrodynamics is a branch of electromagnetism that studies the reciprocal actions between circuits traversed by current or electric charges in motion and the magnetic fields generated (time-varying electromagnetic fields) by such sources. Generally with this term we commonly refer to classical electrodynamics; the quantum or photonic-corpuscular approach to electromagnetic phenomena goes instead under the name of quantum electrodynamics.

Depending on whether we refer to the description of the electromagnetic field given by Maxwell’s equations or to that given by quantum mechanics, we speak of classical electrodynamics or quantum electrodynamics. If the treatment is made in accordance with the theory of relativity, as it is necessary for charges moving with speed close to the speed of light, it is called relativistic electrodynamics.

The study of the electrodynamics phenomena was one of the important steps made by the physics of the nineteenth century, after which great progress would be obtained in the field of electrical engineering. Starting from the first significant experiments of electromagnetic induction, made by Michael Faraday around 1830, it began to understand the close link between electric current and magnetic field. These observations were formalized in a mathematical law by F. Neumann and H. Lenz. Other important contributions in the field of electrodynamics came from Weber, Kirchhoff, Hertz, Lorentz, Maxwell. The latter, in particular, developed the theory of electromagnetism able to explain all classical phenomena of electromagnetic nature both in the stationary case and in the non-stationary case or time-varying. Maxwell’s theory of electromagnetism was later synthesized by Oliver Heaviside through four equations (known as Maxwell’s equations).

## Classical electrodynamics

The theory of **classical electrodynamics** is based on the assumption of Maxwell’s equations passing through the determination of the field at a distance from the sources investigating its propagation in free space and the guided one in guiding media (waveguides), the problems of reflection, refraction, dispersion and those related to electromagnetic radiation from field sources such as electric and magnetic current densities up to understand the relativistic covariance from Maxwell’s equations. It is the basis for understanding many other areas of advanced and applied electromagnetics such as, for example, Antenna Theory.

The dynamic effects of electric charges and currents were studied by Pierre Simon Laplace, Michael Faraday, Heinrich Lenz and many others since the beginning of the nineteenth century, however a coherent and logically complete study of electromagnetic phenomena can be carried out only from the theory of relativity.

In classical electrodynamics, if we place two electric circuits crossed by current near each other, we observe that mechanical forces are exerted between them, which are called electrodynamic because of their electrical origin. They act in a way that depends on the reciprocal position of the circuits, the direction and intensity of the current flowing through them.

## Quantum electrodynamics

**Quantum electrodynamics (QED)** theory, on the other hand, is the quantum theory of the electromagnetic field. QED describes all phenomena involving interacting charged particles by means of the electromagnetic force, at the same time including the theory of special relativity. Mathematically it has the structure of an abelian gauge theory with a U(1) gauge group; from the physical point of view this means that charged particles interact with each other through the exchange of zero mass bosons called photons. It has been called “the jewel of physics” because of its extremely accurate predictions of quantities such as the anomalous magnetic moment of the muon and the Lamb shift of the energy levels of hydrogen.

Contradictions with experience which classical electrodynamics leads to are overcome in quantum electrodynamics. This new theory started from the discovery of the photoelectric effect, which highlighted how the transfer of energy and momentum has a discontinuous character, that is it occurs by indivisible quanta of energy and momentum (Planck hypothesis), and made necessary a reformulation in corpuscular terms of the classical wave description of the electromagnetic field. Its foundations were established mainly by P. A. M. Dirac, W. Heisenberg, W. Pauli, E. Fermi between 1928 and 1930, after that quantum mechanics had its final settlement.

Dirac, in his theory of radiation (1927), gave a completely satisfactory explanation of the phenomena of absorption, emission and diffusion of light by atomic systems. Quantum electrodynamics, which requires an extremely complex mathematical apparatus and is based on the quantization of the electromagnetic field, has succeeded to explain a large number of phenomena of interaction between magnetic fields and matter (Compton effect, annihilation of particle-antiparticle pairs, braking radiation, etc.), but leaves open some problems related to some of its typical calculation procedures. With quantum mechanics constitutes the so called quantum theory.