Do solutions to the Euler Lagrange equation for physical Lagrangians actually minimize the action? In other words, is it known that for all Lagrangians used in application, that the unique solution to the Euler Lagrange equation subject to initial conditions actually is a global minimum for the action functional? How about local minimum? Are there known counterexamples?
Asked
Active
Viewed 309 times
1 Answers
1
Solutions to the equations of motion stationarise the action, but do not need to be minima. For example, sphalerons are saddle points of the action of Electroweak theory.
