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nrqed

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## Main Question or Discussion Point

This is surely a stupid question but here it goes...

An auxiliary field is needed in the Wess-Zumino Lagrangian in order to have the algebra close off-shell. I have a couple of questions about this but let me ask the first one only for now.

Why is this required? The variation of the Lagrangian density gives a total derivative without using the equations of motion, even before the auxiliary fields are introduced. Why do we need to in addition impose that the algebra of the SUSY charges close? I guess I am asking: what would go wrong if the algrebra of charges would not close? This seems to be an issue that is totally unrelated to the invariance of the action but nobody explains what problem would happen if the algebra did not close.

Actually, this is not a purely SUSY question. Why is it important for the algebra of the charges of *any* symmetry to close?

Thanks in advance

An auxiliary field is needed in the Wess-Zumino Lagrangian in order to have the algebra close off-shell. I have a couple of questions about this but let me ask the first one only for now.

Why is this required? The variation of the Lagrangian density gives a total derivative without using the equations of motion, even before the auxiliary fields are introduced. Why do we need to in addition impose that the algebra of the SUSY charges close? I guess I am asking: what would go wrong if the algrebra of charges would not close? This seems to be an issue that is totally unrelated to the invariance of the action but nobody explains what problem would happen if the algebra did not close.

Actually, this is not a purely SUSY question. Why is it important for the algebra of the charges of *any* symmetry to close?

Thanks in advance