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Field transformation under Lorentz group

  1. May 1, 2012 #1
    Hi!
    In Weinberg's book "The quantum theory of fields", chapter2, it states that the transformation
    of a massive particle is
    [tex]
    U(\Lambda)\Psi_{p,\sigma}=
    N\sum\mathcal{D}^{(j)}_{\sigma',\sigma}(W)\Psi_{\Lambda p,\sigma'}
    [/tex]
    where W is an element in the little-group SO(3). But than it states that
    [tex]
    W=L^{-1}(\Lambda p)\Lambda L(p)
    [/tex]
    where L is a 4x4 boost.
    But then W is not in SO(3), it's a 4x4 matrix!! How can this be possible?
     
  2. jcsd
  3. May 1, 2012 #2

    dextercioby

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    Science Advisor
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    W is a 4x4 matrix, an element of the group of 4x4 matrices isomorphic to SO(3).
     
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