Electromagnetism is the fundamental interaction between electric charges and magnetic fields, governing phenomena like electron behavior and magnetism.Maxwell's equations describe how electric and magnetic fields are created by charges and currents and how they mutually generate each other. A changing electric field creates a vortex magnetic field, and a changing magnetic field creates a vortex electric field. This tandem propagates in a vacuum as an electromagnetic wave at speed c = 1/√(μ₀ε₀), where ε₀ and μ₀ are the electric and magnetic constants, measured in experiments with charges and currents. The spectrum of these waves ranges from low-frequency radio waves to gamma rays. Quantum electrodynamics complements the picture, describing the interaction as an exchange of photons—massless particles of light.
The recognition of the connection between electricity and magnetism began with the experiment of H.C. Ørsted (1820), showing that a current causes a magnetic needle to deflect. M. Faraday in 1831 discovered electromagnetic induction—the emergence of current in a circuit when the magnetic flux changes. A brilliant synthesis was accomplished by James Clerk Maxwell: in 1861–64 he formulated a system of equations, adding to Ampère's law the 'displacement current'—a term with the time derivative of the electric field—which ensured consistency and predicted waves. The existence of waves was experimentally confirmed by H. Hertz in 1887. Hendrik Lorentz in 1895 introduced the Lorentz force and created the electron theory, explaining the behavior of charges at the microlevel. The quantum stage was completed in the mid-20th century by the works of R. Feynman, J. Schwinger and S. Tomonaga, who built renormalizable quantum electrodynamics.
Electrodynamics obeys the principle of relativity and is invariant under Lorentz transformations. From Maxwell's equations follows the wave equation for the fields. In quantum electrodynamics, the state of a system is described by a vector in Fock space, creation and annihilation operators for photons are built from the potentials, and the interaction with matter (fermions) is given by the interaction Lagrangian eψ̄γ^μψA_μ (where e is the charge, ψ is the Dirac field, A_μ is the electromagnetic potential). Scattering processes are calculated perturbatively in the fine-structure constant α ≈ 1/137 using Feynman diagrams. At small distances, the effective charge increases (vacuum polarization effect), which has been verified with high accuracy. The classical limit gives the Lorentz force F = q(E + v × B), describing the motion of charged bodies in fields.
All modern communications, from Wi-Fi to satellites, use electromagnetic waves, and without electromagnetism, electric motors, dynamos and MRI scanners would not work. From electric lighting to radio, television and the internet—all this is embodied electromagnetism.
The speed of light c is not just a speed, but a limit embedded in the very laws of electromagnetism; the sizes of atoms and chemistry depend on it, and hence the conditions for life in the Universe.
| a | variable | axion field — axion field |
| E | variable | electric field — electric field volt per metre |
| B | variable | magnetic field — magnetic field strength tesla |
| g_{aγγ} | constant | Strength of the interaction between axions and two photons. — axion photon coupling constant = model-dependent |
| H | variable | Hamiltonian (total energy operator) — hamiltonian joule |
| J | variable | Exchange coupling constant between neighboring spins — exchange coupling joule |
| \mathbf{S}_i | variable | Spin operator at site i — spin operator |
| \mathbf{S}_j | variable | Spin operator at site j — spin operator |
| \sum_{\langle i,j \r | operator | Summation over all pairs of adjacent lattice sites — sum over nearest neighbors |
| H | variable | Hamiltonian of the electron gas — hamiltonian hartree |
| r_i | variable | Position vector of the i-th electron — position bohr |
| r_j | variable | Position vector of the j-th electron — position bohr |
| \nabla_i^2 | operator | Second spatial derivative operator acting on the i-th electron — laplacian operator |
| \sum_i | operator | Summation over the index i — summation |
| \sum_{i<j} | operator | Summation over all pairs with i less than j — summation |



















