Abstract
We consider sharp-time fields and write down, in terms of the fields, simple and explicit expressions for operators with very strong smoothing properties. When applied to any vector in Hilbert space, the resulting vector is in the domain of any power of the space-smeared fields, and it even is entire for the fields. It is shown that in this way one obtains a common dense domain of definition on which the field operators are essentially self-adjoint. Attention is focused on the space S of rapidly decreasing C∞ functions as smearing functions for the fields; here the smoothing operators are simply products of exponentials of the field smeared with Hermite functions.
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