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Oct10-09, 03:57 AM
P: 1,746
Quote Quote by strangerep View Post
IIRC, Haag's original paper basically just pointed out that all known physically-relevant
interactions contained products of creation operators which necessarily lead outside
the free Hilbert space.
Apparently Haag didn't know about the class of "dressed particle" theories in which interactions having only products of creation operators are forbidden. In these theories, each normally-ordered interaction term must have at least two creation operators and at least two annihilation operators. This guarantees that the interaction does not act on the vacuum and one-particle states, so all problems associated with self-interaction, vacuum polarization, etc. are solved trivially.

In my opinion it is very unfortunate that historical development of QFT has ignored this simple and important condition. This omission made QFT more complicated and mysterious than it should be.