Equivariance, variational principles, and the Feynman Integral

Abstract:
We argue that some of the results of variational principles, such as Euler's equations and Noether's theorem can be obtained by geometric means along with equivariance principles, without recourse to the action integral. Partially motivated by this we give an interpretation of Feynman's Integral from the point of view of space-time emergence from a more fundamental theory.