which is the Dirichlet energy of \phi. Classical extrema of the action (the solutions to the Lagrange equations) are then those field configurations that minimize the Dirichlet energy of \phi. Another way to convert this expression into a more easily-recognizable form is to observe that, for a scalar function f:M\to\mathbb{R} one has \mathrm{d}*f=0 and so one may also write
