"Vacuum expectation values of products of neutral operators are discussed. The properties of these distributions arising from , the absence of states and the of the scalar product are determined. The vacuum expectation values are shown to be s of s. Local commutativity of the field is shown to be equivalent to a symmetry property of the analytic functions. The problem of determining a theory of a neutral scalar field given its vacuum expectation values is posed and solved."
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Arthur Wightman,
https://en.wikiquote.org/wiki/Vacuum_expectation_value
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Vacuum expectation value
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