Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Functional variation of Lagrangian densities

  1. Sep 24, 2005 #1
    Why do we treat a scalar field phi and its derivatives as being independent when trying to find a stationary solution for the action?

    Doesn't that give too general solutions?

    Where does the restriction that (d_mu phi) is dependent on phi come back in?
  2. jcsd
  3. Sep 26, 2005 #2


    User Avatar
    Science Advisor
    Homework Helper

    That's the idea. We take things as general as possible. The Lagrangian needs to be a function of positions and velocities treated as independent variables as to allow the passing to the Hamiltonian formalism on one hand and account for the correct description of dynamics on the other. I mean we usually see the lagrangian as the KE-PE function and the KE part involves time derivatives of position (generalized velocities), while the PE part is allowed to depend only on "x" and "t", and not on [itex] \frac{dx}{dt} [/itex].

    Setting things so general we have to use the fundamental variational principle of Hamilton which selects the physically realizable mechanical states,which are of course the solutions of Lagrange equations.

Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?

Similar Discussions: Functional variation of Lagrangian densities
  1. Cp variation (Replies: 1)

  2. Variational technique (Replies: 2)