Electromagnetic four-potential

The electromagnetic four-potential is a four-vector whose time component is related to electric potential and whose spatial components form the magnetic vector potential. Its derivatives encode the electromagnetic field, while gauge transformations leave that field unchanged.

Electromagnetic potential: A scalar or vector function from which electromagnetic fields can be derived. Its electric and magnetic components are unified in the four-potential.
Field strength tensor: The antisymmetric tensor formed from derivatives of a gauge potential. For electromagnetism, it is the derivative combination that converts the four-potential into fields.
James Clerk Maxwell: Scottish physicist whose equations unified electricity, magnetism, and light. His field theory supplied the equations later rewritten using relativistic potentials.
Electrodynamics: The theory of electric and magnetic fields, their sources, and their interactions with matter. The four-potential provides a compact relativistic formulation of classical electrodynamics.
Electric field: A vector field describing the force per unit charge on electric charges. It is derived from the scalar and vector potentials, including the time variation of the vector potential.
Spacetime: A four-dimensional framework combining three spatial dimensions with time. The four-potential has one time component and three spatial components.
Gauge transformation: A change in a gauge potential that preserves the associated physical field. Adding a four-gradient changes the potential without changing the electromagnetic field tensor.
Hendrik Lorentz: Dutch physicist whose transformations describe how space and time coordinates relate between inertial frames. Lorentz transformations exposed the need for electric and magnetic quantities to mix between frames.
Quantum electrodynamics: The quantum field theory describing interactions between charged particles and electromagnetic radiation. Its photon field is quantized through the electromagnetic four-potential.
Magnetic field: A field associated with magnetic forces and changing electric fields. It is obtained as the curl of the spatial vector-potential components.

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