Calculus of variations MOC

Action functional

Let be an -dimensional -manifold. An action functional, also called a variational integral,¹ is a functional on some space of smooth maps from of the form

for some map into top forms

called the Lagrangian.

Further terminology

• A pair consisting of a space of fields and a lagrangian is a Lagrangian field theory.

• A Lagrangian which depends smoothly only on the base point and partial derivatives of up to order is called a Local Lagrangian of order .

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Footnotes

1. 2004. Calculus of variations I, p. 3. ↩