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A local density whose spacetime integral gives the action for a classical or quantum field theory.
wp-physics-lagrangian_densitynlab-physics-lagrangian_densitytong-qftEach relation below ends at this concept.
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Each relation below starts at this concept.
This 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_functionalThis 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.
cambridge-classical-dynamicscern-qft-introwp-physics-classical_field_theorynlab-physics-classical_field_theorywp-physics-lagrangian_mechanicstong-qft