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In an effort to understand the physical implications of the newly discoverednon-trivial directions in scalar field theory, we compute lowest orderscattering amplitudes, cross sections, and the 1-loop effective potential. Tolowest order, the primary effect of the nonpolynomial nature of the theories isa renormalization of the field. The high energy scaling of the 2-->2 crosssection is studied and found to differ significantly from that of pure phi^4theory. From the 1-loop effective potential we determine that in some casesradiative corrections destroy classical symmetry breaking, resulting in a phaseboundary between symmetry broken and unbroken theories. No radiatively inducedsymmetry breaking is observed.Comment: 7 pages, LaTex w/RevTex, PSfig, 3 figure

Cross section and effective potential in asymptotically free scalar field theories