Classical field theory

Classical field theory describes physical systems using fields that vary continuously across space and time, without quantum mechanics. Its equations govern how those fields evolve and interact.

Lagrangian field theory: A formulation of field dynamics using a Lagrangian density and the principle of stationary action. It derives field equations from a compact statement about the system’s action.
Field (physics): A physical quantity assigned to each point in space and time. Classical field theory takes fields, rather than particles alone, as its basic variables.
Classical electrodynamics: The classical theory of electric and magnetic fields and their interactions with charged matter. It is a central field theory governed by Maxwell’s equations.
Quantum field theory: A framework combining quantum mechanics and special relativity in which fields are quantized. It replaces the classical field description with quantum fields and quantum states.
Michael Faraday: An English experimental scientist whose work established key ideas about electromagnetic induction and fields. His field concept helped replace action-at-a-distance accounts of electromagnetic forces.
Euler–Lagrange equation: A differential equation that gives stationary paths or field configurations of an action. Its field form produces equations of motion from a Lagrangian density.
Scalar field: A field assigning a single numerical value to every point in space and time. It is the simplest field type used in classical field models.
Maxwell's equations: The four equations describing how electric and magnetic fields are sourced and evolve. They provide the defining field equations of classical electromagnetism.
Classical mechanics: The nonquantum theory of motion, commonly formulated in terms of particle positions and momenta. It often describes discrete bodies, while field theory assigns variables throughout space.
James Clerk Maxwell: A Scottish physicist who unified electricity, magnetism, and light in a mathematical theory. His equations became a landmark example of a unified classical field theory.

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