For what its worth, physical fermion fields need first and foremost to be Grassmann-valued fields, cf. e.g. this & this Phys.SE posts and the above comment by knzhou. Whether they are real$^1$ or complex-valued depends on the specific theory at hand.

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$^1$ A Grassmann-valued field can be real, i.e. equal to its complex conjugate field.

For what it's worth, physical fermion fields need first and foremost to be Grassmann-valued fields, cf. e.g. this & this Phys.SE posts and the above comment by knzhou. Whether they are real$^1$ or complex-valued depends on the specific theory at hand.

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$^1$ A Grassmann-valued field can be real, i.e. equal to its complex conjugate field.

For what its worth, physical fermion fields need first and foremost to be Grassmann-valued fields, cf. e.g. this & this Phys.SE posts and above comment by knzhou. Whether they are real$^1$ or complex-valued depends on the specific theory at hand.

--

$^1$ A Grassmann-valued field can be real, i.e. equal to its complex conjugate field.

For what its worth, physical fermion fields need first and foremost to be Grassmann-valued fields, cf. e.g. this & this Phys.SE posts and the above comment by knzhou. Whether they are real$^1$ or complex-valued depends on the specific theory at hand.

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$^1$ A Grassmann-valued field can be real, i.e. equal to its complex conjugate field.