Haag's Theorem and Clothed Operators

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Abstract
Haag's theorem is proved. This theorem states—essentially—that a given relativistic field which, at a fixed time, is related by a unitary transformation to the free field, is completely equivalent to the free field throughout all space-time. Previously it had been proved that the vacuum expectation values of the given field equal the free-field ones up to and including the fourfold vacuum expectation value. A corollary to Haag's theorem is derived. The corollary shows that a certain type of relativistic, clothed operator is equivalent to the free field everywhere.

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