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I've been studying Dirac's theory of fermions. A classic topic therein is the proof that the equation is covariant. Invariably authors state that the gamma-matrices have to be considered constants: they do not change under a Lorentz-transformation. I am looking for the reason behind this. It seems to me that if you consider them a vector and the wave-function a scalar then all works out OK. The scalar, vector, tensor, pseudoscalar and pseudovector constructed from the gamma-matrices, the wave-function and its adjoint all have the same value as in the classical approach and transform in the correct fashion. What am I missing?

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# I Why are the gamma-matrices invariant?

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