= Operator-valued distribution
{title2=$\phi(f)=\int\phi(x)f(x)\,d^dx$}
An operator-valued distribution assigns a <linear operator> on a common dense domain to each <smooth> <test function> of <compact support> $f$, continuously and linearly in the appropriate weak sense. A <quantized field> is generally of this type: $\phi(x)$ is formal point notation, while the smeared $\phi(f)$ has operator meaning. Equal-time <canonical commutation relations> and <momentum> oscillators are interpreted after smearing, which avoids treating a <Dirac delta distribution> or a coincident field as a finite ordinary operator. Products at coincident points can need further regularization even when individual smeared fields are defined.
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