On Michele Maggiore book on QFT (page 91) is stated, out of nothing, that "observables are made of an even number of fermionic operator" and similar sentences is in Peskin book (page 56). Is there any physical and mathematical reason for that?
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It is the so-called (fermionic) parity superselection. – Tobias Fünke Mar 05 '24 at 21:03
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@TobiasFunke I think your comment deserves to be elaborated into a full answer, of course, at your convenience. – hyportnex Mar 05 '24 at 22:58
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@hyportnex I agree, but I don't have much time right now. Perhaps later. Also, I couldn't find a good (textbook) reference except one or two lecture notes. – Tobias Fünke Mar 05 '24 at 23:03
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One explanation is that on one hand an observable should be a quantity/operator that could take a value in a measurement in the form of (a tuple of) ordinary numbers.
On the other hand (an odd product of) fermionic operators is Grassmann-odd. A Grassmann-odd number is an indeterminate/variable, which has no value, cf. e.g. this Phys.SE post.
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