*15*

*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 (*t*_{1}, *t*_{2}) its action is

(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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