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A. Neumaier
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It is not an arbitrary choice but the only invariant choice. It makes the mass shells be ##p^2=m^2## rather than ##(p_0-E)^2-p_1^2-p_2^2-p_3^2=m^2##. It is also needed for many other formulas that require ##P## to be covariant.vanhees71 said:it's this arbitrary choice which fixes ##\hat{H}## absolutely
This postulated relation between normal ordering and energy shifts through introducing a central charge is nonexistent, at least it is not in Weinberg's book.vanhees71 said:it's an argument to use "normal ordering" for free-field
Weinberg (on whom you rely for your central charge argument) doesn't use this argument. He introduces normal ordering on p.175 as a normal form in which to represent arbitrary field operators, which is indeed the natural thing to do. He later gives a complete discussion of the free field without any reference to normal ordering. The next mention of the term is on p.200, where he uses it to normally order the interaction term in the classical action. Not in order to make the vacuum energy zero, which he obtains on p.65 (case (f)) as an automatic consequence of his definitions (2.4.18-24) of the commutation relations.
I meant, hardly relevant for the subject of his book, relativistic QFT.vanhees71 said:the starred sections in Weinberg's books are not "hardly relevant" but "not so relevant at a first read".