classical field theory


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Classical field theory

The mathematical discipline that studies the behavior of distributions of matter and energy when their discrete nature can be ignored; also known as continuum physics or continuum mechanics. The discrete nature of matter refers to its molecular nature, and that of energy to the quantum nature of force fields and of the mechanical vibrations that exist in any sample of matter. The theory is normally valid when the sample is of laboratory size or larger, and when the number of quanta present is also very large. See Phonon, Photon, Quantum mechanics

Classical field theories can be formulated by the molecular approach, which seeks to derive the macroscopic (bulk) properties by taking local averages of microscopic quantities, or by the phenomenological approach, which ignores the microscopic nature of the sample and uses properties directly measurable with laboratory equipment. Although the microscopic treatment sometimes yields profounder insights, the phenomenological approach can use partial differential equations since neglecting the microscopic structure allows quantities such as density and pressure to be expressed by continuously varying numbers.

Examples of classical field theories include the deformation of solids, flow of fluids, heat transfer, electromagnetism, and gravitation. Solving the equations has produced a vast body of mathematics. Computers have aided in special calculations, but many mathematicians are working on the analytical theory of partial differential equations, and new results continue to be produced.

classical field theory

[′klas·ə·kəl ′fēld ‚thē·ə·rē]
(physics)
The study of distributions of energy, matter, and other physical quantities under circumstances where their discrete nature is unimportant, and they may be regarded as (in general, complex) continuous functions of position. Also known as c-number theory; continuum mechanics; continuum physics.
References in periodicals archive ?
Among the topics are a non-arithmetic derivation of the Selberg trace formula, the Hamiltonian reduction of unconstrained and constrained systems, discrete evolution for the zero modes of the quantum Liouville model, spectrum and scattering excitations in the one-dimensional isotropic Heisenberg model, and stable knot-like structures in classical field theory.
In relativistic classical field theory, all causality questions are resolvable systematically.
Beyond these problems, the use of one particle lagrangians and couplings that get promoted to many body interacting theory through canonical quantization or propagator methods lead to a kind of conceptual disconnect that makes the solid implications of classical field theory, e.
If we are going to seek a classical field theory approach to this problem we need another mechanism.
He covers non-relativistic quantum mechanics, thermal and statistical physics, many-body theory, classical field theory and relativity, and relativistic quantum mechanics and gauge theories.
They believe that, just as classical field theory was overshadowed by quantum theory and particle physics, the integrative systems-level physiology gave way to cellular and molecular biology.
of Geneva) covers Lorentz and Poincare symmetries in quantum field theory, classical field theory, quantization of free fields, perturbation theory and Feynman diagrams, cross-section and decay rates, quantum electrodynamics, the low-energy limit of the electroweak theory, path integral quantization, non- abelian gauge theories, and spontaneous symmetry breaking.
Let us first acquaint ourselves with the theory of phase transitions in classical physics, and in particular in the context of classical field theory.
That is: there are infinitely many unitarily inequivalent quantum field theories which are quantizations of any given classical field theory.
His topics are elements of classical field theory, global symmetries, local symmetry and constraint theory, the functional integral formulation of field theory, non-abelian gauge symmetry, discrete symmetries, spontaneous symmetry breaking, and the anomalous breaking of chiral symmetry on quantization.
Understanding of classical field theory underlies understanding of quantum field theory, and this text covers the subject beginning with a chapter on differential calculus on fiber bundles and proceeding with chapters on Lagrangian field theory, Grassmann-graded Lagrangian field theory, Lagrangian BRST theory, gauge theory on principal bundles, gravitation theory on natural bundles, spinor fields, topological field theories, and covariant Hamiltonian field theory.
Examples are mainly drawn from classical mechanics, classical field theory, classical electrodynamics, quantum mechanics, quantum statistical mechanics, and quantum field theory.

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