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Weyl ordering of the hamiltonian

  1. Oct 19, 2011 #1
    Hi , I can't understand the general formula for weyl ordering of the hamiltonian . It is written in Srednicki field theory book in page 68 . Can someone explain how to derive this formula ?
     
  2. jcsd
  3. Oct 19, 2011 #2

    tom.stoer

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    You can't derive a specific ordering of the Hamiltonian; the ordering of operators is a quantization ambiguity which has no classical counterpart. Usually you have p²/2m for the kinetic energy of a particle but there is no qm principle which tells you that (px)(p/x)/2m is wrong. Different ordering schemes may result in different physics and you have to use an additional, independent physical principle in orer to select the "correct" one.

    In case of a curved manifold with a free particle moving on that manifold one reasonable idea is to use the Laplace-Beltrami operator as kinetic energy; this results in a unique operator ordering.

    Perhaps Srednicki explains something like that ...
     
  4. Oct 20, 2011 #3

    Bill_K

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    The Weyl ordering tries to define a general prescription for operator ordering: complete symmetrization.

    O(qn pm) ≡ 2-n Σ qn−i pm qi where the sum runs i=0 to n.

    But difficult questions like operator ordering are a reason that people turned away from Langrangian formulation and were led instead to path integrals.
     
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