Abstract
This paper examines the operator product using the example of scalar field theories with unstable vacuums. We find that an operator-product expansion about the unstable vacuum, with the additional assumption that nontrivial operators subtracted with respect to this vacuum have nonvanishing expectation value in the physical vacuum, does not reproduce the predictions of the operator-product expansion about the stable vacuum, except for the leading-twist contribution. We discuss the implications of this for applications of the operator-product expansion in QCD.
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