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Unitary spacetime translation operator

  1. Jun 29, 2013 #1
    Srednicki eqn. (2.23) and (2.24) states: We can make this a little fancier by defining the unitary spacetime translation operator

    [tex] T(a) \equiv \exp(-iP^\mu a_\mu/ \hbar) [/tex]

    Then we have
    [tex] T(a)^{-1} \phi(x) T(a) = \phi(x-a) [/tex]

    How do we get the second equation from the first equation?
  2. jcsd
  3. Jun 29, 2013 #2
    If you believe eq. (2.22) just above this, then you can plug ##\phi(x) = e^{-iPx/\hbar}\phi(0)e^{+iPx/\hbar}## into eq. (2.24). Then using the definition of ##T(a)## you can verify that eq. (2.24) holds.
  4. Jun 30, 2013 #3
    Lovely answer.
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