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I need clear up relation between a lagrangian density and coupled Euler-Lagrange equations a posteriori them covariance.

If has a lagrangian scalar character, then Euler-Lagrange equations are covariant (=tensor) too. This is clear!

Me question is:Do it validity vice versa?

Precisely. Euler-Lagrangian are tensor's equs. Must be coupled lagrangian necessary in scalar form??? (for unspecific divergent term in a lagrangian.)

More accurately, do exist such divergent term in lagrange density, so that whole lagrangian is a scalar form for coupled tensor's E-L equs?

Or, is possibile have tensor's Euler-Lagrange equations and simultaneously theirs lagrangian is NOT scalar (for any divergent term)?

Sorry for me terrible english:)

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# Lagrangian and covariant (tensor) character Euler equations

Can you offer guidance or do you also need help?

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