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Consider a general Euclidean QFT (or its lattice regularization).

Given a list of all correlators of operators in this theory, and given that they are reflection-positive, how can one explicitly reconstruct the Hilbert space of the real-time theory on any time slice in such a way that the contact terms that appear at coincident points in correlators are also uniquely fixed?

Inclusion of citations to key references is appreciated.

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  • $\begingroup$ Which contact terms are you talking about? What you are asking is covered by Osterwalder-Schrader reconstruction theorem, apart from the contact terms. "Contact terms" in Wightman functions are uniquely fixed by analyticity and the contact terms in time-ordered correlators are not really related to the Hilbert space. $\endgroup$ Commented Sep 30 at 12:54

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