The Lorentz group generators, in any representation, satisfy the commutation relation(adsbygoogle = window.adsbygoogle || []).push({});

[tex]

[S^{\mu \nu}, S^{\rho \sigma}] = i \left( g^{\nu \rho}S^{\mu \sigma} -g^{\mu \rho} S^{\nu \sigma} -g^{\nu \sigma}S^{\mu \rho} +g^{\mu \sigma} S^{\nu \rho} \right)

[/tex]

and the Lorentz transformation is

[tex]

\Lambda=\exp(-i \omega_{\mu \nu} S^{\mu \nu}/2)

[/tex]

My question is: is it possible to prove the formula for the generators (the first formula I wrote), from the definition of the Lorentz group

[tex]

\Lambda^T g \Lambda =g

[/tex]

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# Lorentz generators algebra

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