I have very simple questions. Although these are simple but I am confused. So if I start with a lagrangian of the following form $$ \mathcal{L} = \partial^{\mu}\phi \partial_{\mu} \phi^{*} -m^{2} \phi^{*} \phi $$ then I get a current for the global invariance of the lagrangian and that is of the form $$ J^{\mu}=i(\partial^{\mu} \phi \phi^{*} -\partial^{\mu} \phi^{*} \phi) ... (1 )$$Then if I demand local gauge invariance then definitely we get gauge field terms in the lagrangian. Then if we find an expression of current for the global invariance of ##\phi## field we get expression $$ J^{\mu}=i(D^{\mu}\phi \phi^{*} -D^{\mu}\phi^{*} \phi) ...(2) $$ And there is other expression for current which is conserved on local gauge invariance but they are not physical since they are not gauge invariant. But global ones are gauge invariant and therefore it's ok to have their physical presence in the theory. But I am confused that which one is physical 1 or 2 or both??? One more thing is these currents or the global charge defined from it is due to the symmetry of the theory ,not external ones. So in principle we don't see them. Is this right?(adsbygoogle = window.adsbygoogle || []).push({});

Thanks.

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# Which current is physical?

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