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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.
The topic broadly splits into equations of classical field theory and quantum field theory. Classical field equations describe many physical properties like temperature of a substance, velocity of a fluid, stresses in an elastic material, electric and magnetic fields from a current, etc. [1] They also describe the fundamental forces of nature ...
(3) The theory I propose may therefore be called a theory of the Electromagnetic Field, because it has to do with the space in the neighbourhood of the electric and magnetic bodies, and it may be called a Dynamical Theory, because it assumes that in that space there is matter in motion, by which the observed electromagnetic phenomena are produced
The series commenced with What You Need to Know (above) reissued under the title Classical Mechanics: The Theoretical Minimum. The series presently stands at four books (as of early 2023) covering the first four of six core courses devoted to: classical mechanics , quantum mechanics , special relativity and classical field theory , general ...
The classical Lagrangian density describes an infinity of coupled harmonic oscillators, labelled by x which is now a label (and not the displacement dynamical variable to be quantized), denoted by the classical field φ, = () (), where V(φ) is a potential term, often taken to be a polynomial or monomial of degree 3 or higher.
Like many other classical unified field theorists, Eddington considered that in the Einstein field equations for general relativity the stress–energy tensor, which represents matter/energy, was merely provisional, and that in a truly unified theory the source term would automatically arise as some aspect of the free-space field equations.
In mathematical physics, covariant classical field theory represents classical fields by sections of fiber bundles, and their dynamics is phrased in the context of a finite-dimensional space of fields. Nowadays, it is well known that [citation needed] jet bundles and the variational bicomplex are the correct domain for such a description.
Cadabra is a computer algebra system designed specifically for the solution of problems encountered in classical field theory, quantum field theory and string theory. The first version of Cadabra was developed around 2001 for computing higher-derivative string theory correction to supergravity. [2] [3]