Cross Section and Effective Potential in Asymptotically Free Scalar Field Theories

Abstract

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.

7 pages, LaTex w/RevTex, PSfig, 3 figures

References in corpus (2)

• Non-Trivial Directions for Scalar Fields
• Halpern-Huang directions in effective scalar field theory

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• Flow equation for Halpern-Huang directions of scalar O(N) models
• Nonpolynomial Normal Modes of the Renormalization Group in the Presence of a Constant Vector Potential Background