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Reference.org
Classical field theory
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<p>A classical field theory is a <a href="/facts/Physical_theory/Cs2Y12rQ">physical theory</a> that predicts how one or more <a href="/facts/Field_(physics)/FJdAKeRA">fields in physics</a> interact with matter through field equations, without considering <a href="/facts/Quantum_mechanics/BRc3Mzgr">effects of quantization</a>; theories that incorporate quantum mechanics are called <a href="/facts/Quantum_field_theory/VoewsNJV">quantum field theories</a>. In most contexts, 'classical field theory' is specifically intended to describe <a href="/facts/Electromagnetism/oAkmALHT">electromagnetism</a> and <a href="/facts/Gravitation/bqAN7DdQ">gravitation</a>, two of the <a href="/facts/Fundamental_force/WrFEJaFl">fundamental forces</a> of nature. </p><p>A physical field can be thought of as the assignment of a <a href="/facts/Physical_quantity/S8pWBEpK">physical quantity</a> at each point of <a href="/facts/Space/tq6LUM3C">space</a> and <a href="/facts/Time/HceJKUGB">time</a>. For example, in a weather forecast, the wind velocity during a day over a country is described by assigning a <a href="/facts/Vector_(mathematics_and_physics)/U8mM7A5F">vector</a> 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 <a href="/facts/Vector_field/ccFNuPPp">vector field</a>. As the day progresses, the directions in which the vectors point change as the directions of the wind change. </p><p>The first field theories, <a href="/facts/Newtonian_gravitation/F6qH2XC3">Newtonian gravitation</a> and <a href="/facts/Maxwell%2527s_equations/LfJ1drHS">Maxwell's equations</a> of electromagnetic fields were developed in classical physics before the advent of <a href="/facts/Relativity_theory/qGHj3eTC">relativity theory</a> in 1905, and had to be revised to be consistent with that theory. Consequently, classical field theories are usually categorized as <i>non-relativistic</i> and <i>relativistic</i>. Modern field theories are usually expressed using the mathematics of <a href="/facts/Tensor_calculus/VqecNRwX">tensor calculus</a>. A more recent alternative mathematical formalism describes classical fields as sections of <a href="/facts/Mathematical_object/Juhyow9M">mathematical objects</a> called <a href="/facts/Fiber_bundle/SJ7Ek6cI">fiber bundles</a>. </p>