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A derivative of a functional with respect to a function or field, defined through its first variation.
Existence and representation depend on the function space, topology, measure, and boundary conditions.
wp-functional_derivativenlab-functional_derivativetong-qftEach relation below ends at this concept.
This is an authored directed relation from the source endpoint to the target endpoint.
The functional derivative represents the first variation when such a representation exists.
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-calculus_of_variationsnlab-calculus_of_variationscambridge-classical-dynamicstong-qftwp-functional_derivativenlab-functional_derivativeEach relation below starts at this concept.
This is an authored directed relation from the source endpoint to the target endpoint.
Euler–Lagrange field equations are obtained by setting the functional derivative of the action to zero.
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.
wp-functional_derivativenlab-functional_derivativetong-qftwp-physics-euler_lagrange_equationnlab-physics-euler_lagrange_equationcambridge-classical-dynamics