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Or you can call it classical field, so that everybody is happy.PatrickUrania said:
Why are the gamma-matrices invariant?
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In summary, The Dirac equation is covariant and the gamma-matrices are considered constant because they do not change under a Lorentz transformation. The Lorentz transformation acts on everything in spacetime, including the momentum operator and the wavefunction, which can be viewed as a set of complex scalars. However, there are alternative formalisms, such as the one proposed in the paper by Demystifier, that view the gamma-matrices as transforming under Lorentz transformations, but the physical content of the Dirac equation remains unchanged regardless of which formalism is used. The reason why the traditional way is still widely used may be due to its familiarity and practicality, as well as the fact that the new formalism is
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Well, but then you need a lot of handwaving, called "hole theory", and you end up with something that's a complicated version of quantum field theory. That's why I prefer to say relativistic QT should be introduced as relativistic QFT right away.