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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?

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# Field transformation under Lorentz group

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