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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 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 relativity, cosmology, and statistical mechanics. Videos for all of these courses are available online.
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 ...
Attempts to create a unified field theory based on classical physics are classical unified field theories. During the years between the two World Wars , the idea of unification of gravity with electromagnetism was actively pursued by several mathematicians and physicists like Einstein, Theodor Kaluza , [ 19 ] Hermann Weyl , [ 20 ] Arthur ...
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.
semiclassical gravity: quantum field theory within a classical curved gravitational background (see general relativity). quantum chaos; quantization of classical chaotic systems. magnetic properties of materials and astrophysical bodies under the effect of large magnetic fields (see for example De Haas–Van Alphen effect)
Landau's accomplishments include the independent co-discovery of the density matrix method in quantum mechanics (alongside John von Neumann), the quantum mechanical theory of diamagnetism, the theory of superfluidity, the theory of second-order phase transitions, the Ginzburg–Landau theory of superconductivity, the theory of Fermi liquids ...
When the canonical quantization procedure is applied to a field, such as the electromagnetic field, the classical field variables become quantum operators. Thus, the normal modes comprising the amplitude of the field are simple oscillators, each of which is quantized in standard first quantization, above, without ambiguity.