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A general class of quantum fields without cut-offs in two space-time dimensions

Authors:	Raphael Høegh-Krohn

Institution:	(1) Joseph Henry Laboratories, Princeton University, Princeton, N.J.;(2) Matematisk Institutt, Universitetet I Oslo, Blindern, Postboks 1053, Oslo 3, Norway

Abstract:	We consider a selfinteracting boson field in two space-time dimensions, with interaction densities of the form:V((x)): where (x) is a scalar boson field, andV() is a real positive function of exponential type. We define the space cut-off interaction by $V_r = \int\limits_{\left\| x \right\| \leqq r} {:V(\varphi (x))} :dx$ and prove thatH _r=H ₀+V _r, whereH ₀ is the free energy, is essentially self adjoint. This permits us to take away the space cut-off and we obtain a quantum field free of cut-offs.At leave from Mathematical Institute, Oslo University.This research partially sponsored by the Air Force Office of Scientific Research under Contract AF 49(638)1545.

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