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I'm currently reading Ryder - Quantum Field Theory and am a bit confused about his discussion on the correpsondence between Lorentz transformations and SL(2,C) transformations on 2-spinor.

He writes that the Lie algebra of Lorentz transformations can be satisfied by setting

[tex]\vec{K} =\pm \frac{i \vec{\sigma}}{2}. [/tex]

Here it seems as if the dimensions are mixed up. The Pauli matrices are 2 times 2 while the Loretnz generators are 4 times 4.

Secondly he argues that the Lorentzgroup can be ''factorized'' into [tex]SU(2) \times SU(2)[/tex] but how come this goes along with the fact that the Loretnz group is non-compact.

It seems as if we take the product group of two compact group the resulting group is compact?

Am I wrong about this?

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# About the Lie algebra of our Lorentz group

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