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Physics
High Energy, Nuclear, Particle Physics
Homomorphism SL(2,C) with restricted Lorentz
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[QUOTE="ChrisVer, post: 5447104, member: 494486"] A map of the form: [itex] \phi : A \rightarrow B[/itex] [itex] a \rightarrow b=\phi(a)[/itex] is roughly speaking an homomorphism if for elements [itex]x, y \in A[/itex] the [itex] \phi(x) \cdot \phi(y) = \phi(x*y)[/itex] and that's why the comment about multiplication. As for the proof of your last equation in post2, if I recall well you can prove it better by writting the traces with summed indices: [itex] G_{ai} \sigma_{ia}^\mu \bar{\sigma}^\mu_{jb} H_{bj}[/itex] and then using seperately the [itex]\sigma^0, \sigma^k[/itex]'s and use their completeness relation (generalization of the : [URL]https://en.wikipedia.org/wiki/Pauli_matrices#Completeness_relation[/URL])... but I don't really remember the complete proof... [/QUOTE]
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Physics
High Energy, Nuclear, Particle Physics
Homomorphism SL(2,C) with restricted Lorentz
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