Generating Functions

Abstract

If S is a real valued function defined on the manifold AT, then its differential dS can be considered as a mapping dS : N → T ^* N from N into its cotangent space. The image L _S of this mapping is then an exact Lagrangian submanifold of T ^* N: Equation 1

$$ {(dS)^*}(pdq) = dS $$

and consequently (dS)^*(dp⋀dq) = 0. The function S is called a naive generating function for L _S.