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A functional of a history or field configuration whose stationary points satisfy equations of motion.
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This is an authored directed relation from the source endpoint to the target endpoint.
For particle mechanics, .
Apply a standard functorial or canonical construction whose output is not merely a reduct of the input and is not generally an equivalent presentation of the same object.
wp-physics-lagrangian_mechanicsnlab-physics-lagrangianwp-physics-action_functionalnlab-physics-action_functionalThis is an authored directed relation from the source endpoint to the target endpoint.
For a local field theory, .
Apply a standard functorial or canonical construction whose output is not merely a reduct of the input and is not generally an equivalent presentation of the same object.
wp-physics-lagrangian_densitynlab-physics-lagrangian_densitywp-physics-action_functionalnlab-physics-action_functionalEach relation below starts at this concept.
This is an authored directed relation from the source endpoint to the target endpoint.
Path-integral quantization uses the classical action in a formal or regulated sum over histories, typically with phase ; making the construction rigorous depends on the theory and signature.
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.
wp-physics-path_integral_quantizationnlab-physics-path_integral_quantizationThis is an authored directed relation from the source endpoint to the target endpoint.
Stationarity of the action supplies the variational dynamical principle.
The source supplies a substantive formal ingredient, dynamical sector, law, field content, or mechanism of the target theoretical framework.
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