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Lagrangian and covariant (tensor) character Euler equations

  1. Sep 12, 2009 #1
    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:)
    Last edited: Sep 12, 2009
  2. jcsd
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