Hello! I read that the for the lie algebra of the Lorentz group we can parametrize the generators as an antisymmetric tensor ##J^{\mu \nu}## and the parameters as an another antisymmetric tensor ##\omega_{\mu \nu}## and a general transformation would be ##\Lambda = exp(-\frac{i}{2} \omega_{\mu \nu} J^{\mu \nu})##. So based on Einstein notation, this would mean ##\Lambda = exp(-\frac{i}{2} (\omega_{00} J^{00} + \omega_{01} J^{01} + ... ))##. But for example ##\omega_{00}## and ##J^{00}## are numbers, so in the end we will end up with a complex number in the exponential and now with a (4x4 most probably) matrix. Can someone explain to me what I do wrong in reading this notation? Thank you!(adsbygoogle = window.adsbygoogle || []).push({});

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# I Lie Algebra of Lorentz group

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