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A theory in which continuously distributed fields obey classical equations of motion. A classical field theory may be formulated independently or arise as an effective, mean-field, or semiclassical description in an appropriate regime.
Quantizing an appropriate classical field theory is a principal route to a quantum field theory, while classical field equations can reappear as semiclassical or low-fluctuation limits.
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This is an authored directed relation from the source endpoint to the target endpoint.
For a classical field theory admitting a local action principle, the Lagrangian density is a formal component whose spacetime integral yields the action and field Euler–Lagrange equations.
The source supplies a substantive formal ingredient, dynamical sector, law, field content, or mechanism of the target theoretical framework.
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Classical field dynamics is normally expressed through systems of PDEs.
A mathematical concept supplies part of the formal language, state space, representation, or analytic machinery used by a scientific or mathematical-physics concept. The source is the mathematical predecessor; this does not claim that physical content follows from mathematics alone.
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Classical field theory describes continuous fields on spacetime without quantizing their dynamical degrees of freedom.
A more specific theory, model, entity class, or regime is obtained by restricting or extending the scope of a broader framework.
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Sobolev spaces formulate finite-energy fields and weak solutions of field equations.
A mathematical concept supplies part of the formal language, state space, representation, or analytic machinery used by a scientific or mathematical-physics concept. The source is the mathematical predecessor; this does not claim that physical content follows from mathematics alone.
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This is an authored directed relation from the source endpoint to the target endpoint.
Canonical quantization promotes field variables and momenta to operators, when the constraint and gauge structure can be handled.
A classical system or field theory is used to construct a quantum theory through a stated quantization procedure. Quantization need not be unique and is not guaranteed to preserve every classical structure.
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Classical electromagnetism is a relativistic classical field theory.
A more specific theory, model, entity class, or regime is obtained by restricting or extending the scope of a broader framework.
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Path-integral methods construct quantum amplitudes from the classical action after gauge fixing and regularization as needed.
A classical system or field theory is used to construct a quantum theory through a stated quantization procedure. Quantization need not be unique and is not guaranteed to preserve every classical structure.
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Canonical or path-integral quantization of a classical field theory is a standard route to a QFT, although quantum consistency and renormalization can alter the admissible theory.
A classical system or field theory is used to construct a quantum theory through a stated quantization procedure. Quantization need not be unique and is not guaranteed to preserve every classical structure.
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