- #1
Kontilera
- 179
- 24
Hello!
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?
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?