Abstract
We consider a boson field ϕ(x) under an interaction of the form\(\mathop \smallint \limits_{R^3 } \) V(ϕ(x))dx, whereV(α) is a bounded continuous real function of a real variable α. IfV(α) has a uniformly continuous and bounded first derivative, we prove that the Heisenberg picture field exists as weak limits of the Heisenberg picture fields corresponding to the cut-off interaction.
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Høegh-Krohn, R. Boson fields under a general class of local relativistic invariant interactions. Commun.Math. Phys. 14, 171–184 (1969). https://doi.org/10.1007/BF01645418
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DOI: https://doi.org/10.1007/BF01645418