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I What does it means for a physical theory to have Hamiltonian, if it is formulated in Lagrangian form

  1. Dec 20, 2017 #1
    What does it means for a physical theory to have hamiltonian, if it is formulated in lagrangian form? Why doesn't someone just apply the lagrangian transformation to the theory, and therefore its hamiltonian is automatically gotten?
     
  2. jcsd
  3. Dec 20, 2017 #2

    Orodruin

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    Can you be more specific and give a specific example?

    In general, you can get to the Hamiltonian formulation of the same theory by applying the Legendre transform (which is what I assume that you mean) to your Lagrangian. In order for this to work, the Legendre transform needs to exist, which in turn requires the Lagrangian to be a convex function of the time derivative of your generalised coordinates.
     
  4. Dec 20, 2017 #3
    Ah, sorry. Legendre transformation. That was what I meant. But doesn't it always exist?
     
  5. Dec 20, 2017 #4

    Orodruin

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    No. See the wikipedia page.
     
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