Poisson Bracket Filter for the Effective Lagrangians

Abstract

One might think that a Lagrangian function of any form is suitable for a complete description of a process. Indeed, it does not matter in terms of the equations of motion, but it seems that this is not enough. Expressions with Poisson brackets are displayed as required fulfillment filters. In the case of the Schrödinger equation for a free particle, we show what we have to be careful about.