Editing Classical field theory (section)

{{short description|Physical theory describing classical fields}}
{{Classical mechanics}}
A '''classical field theory''' is a [[physical theory]] that predicts how one or more [[field (physics)|fields in physics]] interact with matter through '''field equations''', without considering [[Quantum mechanics|effects of quantization]]; theories that incorporate quantum mechanics are called [[quantum field theory|quantum field theories]]. In most contexts, 'classical field theory' is specifically intended to describe [[electromagnetism]] and [[gravitation]], two of the [[fundamental force]]s of nature.

A physical field can be thought of as the assignment of a [[physical quantity]] at each point of [[space]] and [[time]]. For example, in a weather forecast, the wind velocity during a day over a country is described by assigning a [[vector (mathematics and physics)|vector]] to each point in space. Each vector represents the direction of the movement of air at that point, so the set of all wind vectors in an area at a given point in time constitutes a [[vector field]]. As the day progresses, the directions in which the vectors point change as the directions of the wind change.

The first field theories, [[Newtonian gravitation]] and [[Maxwell's equations]] of electromagnetic fields were developed in classical physics before the advent of [[relativity theory]] in 1905, and had to be revised to be consistent with that theory. Consequently, classical field theories are usually categorized as ''non-relativistic'' and ''relativistic''. Modern field theories are usually expressed using the mathematics of [[tensor calculus]]. A more recent alternative mathematical formalism describes classical fields as sections of [[mathematical object]]s called [[fiber bundle]]s.