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Evoluation Operators

  1. Jan 9, 2010 #1
    Two quantum mechanics operators are infinitesimal translation and time evulotion operators.Is there an infinitesimal translation time evolution operator similar to relativistic mechanics?
     
  2. jcsd
  3. Jan 9, 2010 #2

    Fredrik

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    The operator that does translations in spacetime can be written as

    [tex]e^{-ia_\mu P^\mu}[/itex]

    where P is the four-momentum. (The 0th component is the Hamiltonian). Note that there's a sum over [itex]\mu[/itex] from 0 to 3 in the exponent. The notational convention is to not write any summation sigmas when the summation index occurs exactly twice.
     
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