If I have a lagrangian which has terms of the form ##\Psi^{\dagger}_\mu \Psi^\mu## then I can decompose the n complex ##\Psi## fields into 2n real fields by ##\Psi_\mu = \eta_{2\mu+1} + i\eta_{2\mu}##. When I look at the lagrangian now it seems to have SO(2n) symmetry from mixing the 2n real fields.(adsbygoogle = window.adsbygoogle || []).push({});

Is there any obvious choice of representing SO(2n) on the n complex ##\Psi## fields explicitly?

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# I SO(2n) representation on n complex fields

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