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I am learning QFT and is baffled by a minor problem.

The electron and the positron should be distinguishable, as they have different charges. So why do their creation operators anti-commute? They should commute with each other, just like the creation operators of the electron and the proton commute with each other.

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As far as I remember, you can choose creation operators of different fermions to commute or to anti-commute, both choices should provide correct results if used consistently.

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