A classical field theory is a physical theory that predicts how one or more fields in physics interact with matter through field equations, without considering effects of quantization; theories that incorporate quantum mechanics are called quantum field theories. In most contexts, 'classical field theory' is specifically intended to describe electromagnetism and gravitation, two of the fundamental forces 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 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 objects called fiber bundles.
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A classicalfieldtheory is a physical theory that predicts how one or more fields in physics interact with matter through field equations, without considering...
physics are described in the article on classical unified fieldtheories. The goal of a unified fieldtheory has led to a great deal of progress for future...
In theoretical physics, quantum fieldtheory (QFT) is a theoretical framework that combines classicalfieldtheory, special relativity, and quantum mechanics...
paradigm, which includes classical mechanics and relativity. Likewise, classicalfieldtheories, such as general relativity and classical electromagnetism, are...
In mathematical physics, covariant classicalfieldtheory represents classicalfields by sections of fiber bundles, and their dynamics is phrased in the...
nature – a unified fieldtheory. Classical unified fieldtheories are attempts to create a unified fieldtheory based on classical physics. In particular...
Hamiltonian fieldtheory is the field-theoretic analogue to classical Hamiltonian mechanics. It is a formalism in classicalfieldtheory alongside Lagrangian...
currents using an extension of the classical Newtonian model. It is, therefore, a classicalfieldtheory. The theory provides a description of electromagnetic...
In physics, a gauge theory is a type of fieldtheory in which the Lagrangian, and hence the dynamics of the system itself, do not change under local transformations...
employs fields in the physical sense, consisting of three types: Classicalfieldtheory, the theory and dynamics of classicalfields Quantum fieldtheory, the...
referred to as "the field equation". The topic broadly splits into equations of classicalfieldtheory and quantum fieldtheory. Classicalfield equations describe...
ISBN 978-0-486-65067-8. Synge, J. L. (1960). "Classical dynamics". In Flügge, S. (ed.). Principles of Classical Mechanics and FieldTheory / Prinzipien der Klassischen...
physics, scalar fieldtheory can refer to a relativistically invariant classical or quantum theory of scalar fields. A scalar field is invariant under...
self-similarity. In classicalfieldtheory, scale invariance most commonly applies to the invariance of a whole theory under dilatations. Such theories typically...
as is the case in classical mechanics. This is incompatible with classical mechanics and special relativity because in those theories inertially moving...
magnetic field and to its direction of motion. The electromagnetic field is described by classical electrodynamics, an example of a classicalfieldtheory. This...
older classical principles. Action principles are the basis for Feynman's version of quantum mechanics, general relativity and quantum fieldtheory. This...
some field equation. Note: This article focuses on relativistic classicalfieldtheories of gravitation. The best known relativistic classicalfield theory...
Classical control theory is a branch of control theory that deals with the behavior of dynamical systems with inputs, and how their behavior is modified...
procedure for quantizing a classicaltheory, while attempting to preserve the formal structure, such as symmetries, of the classicaltheory to the greatest extent...
Algebraic quantum fieldtheory (AQFT) is an application to local quantum physics of C*-algebra theory. Also referred to as the Haag–Kastler axiomatic...
the history of quantum fieldtheory starts with its creation by Paul Dirac, when he attempted to quantize the electromagnetic field in the late 1920s. Major...
fieldtheory in curved spacetime (QFTCS) is an extension of quantum fieldtheory from Minkowski spacetime to a general curved spacetime. This theory uses...
In physics, Liouville fieldtheory (or simply Liouville theory) is a two-dimensional conformal fieldtheory whose classical equation of motion is a generalization...
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