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Physical Mathematics by Kevin Cahill

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15

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Functional derivatives

15.1 Functionals

A functional G[f] is a map from a space of functions to a set of numbers. For instance, the action functional S[q] for a particle in one dimension maps the coordinate q(t), which is a function of the time t, into a number – the action of the process. If the particle has mass m and is moving slowly and freely, then for the interval (t1, t2) its action is

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(15.1)

If the particle is moving in a potential V(q(t)), then its action is

(15.2)

15.2 Functional derivatives

A functional derivative ...

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