  In an effort to understand the physical implications of the newly discovered
non-trivial directions in scalar field theory, we compute lowest order
scattering amplitudes, cross sections, and the 1-loop effective potential. To
lowest order, the primary effect of the nonpolynomial nature of the theories is
a renormalization of the field. The high energy scaling of the 2-->2 cross
section is studied and found to differ significantly from that of pure phi^4
theory. From the 1-loop effective potential we determine that in some cases
radiative corrections destroy classical symmetry breaking, resulting in a phase
boundary between symmetry broken and unbroken theories. No radiatively induced
symmetry breaking is observed.
