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Why do we study symmetries only via Noether conserved currents?
In general, we say a transformation is a symmetry of a theory if it leaves the action invariant, i.e. if
$$S \to S' = S,$$
up to, perhaps, a boundary term (b.t.). However, it is known (see e.g. this ...
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If the lagrangian density changes by a total derivative of the lagrangian density
When we derive energy momentum tensor current by actively transforming field. We see that lagrangian ( density) changes by a total derivative of the lagrangian. If a total derivative of the function ...
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