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- the lagrangian (or if not the lagrangian then the least action) must be chosen so that it is gauge invariant

- the lagrangian should contain terms like (dx/dt) squared for single particles where x represents phase space and correspondingly for a field ∅, with terms in d∅/dt squared

- for relativistic systems the lagrangian (or the least action?) should also be lorenz invariant

Then through a process of experimentation the lagrangian and corresponding least action can be found.

This is my understanding so far and I am asking if this (ie any of the above) is correct.

Many thanks