Renormalization Group Analysis of Scalar Field

We employ Wilson's renormalization group procedure in an attempt to classify and understand the physics of the continuum limits of scalar field theories. Analysis of the flows near the Gaussian fixed point reveals the existence of an infinite set of asymptotically free continuum limits. We study the associated physics by calculating scattering cross sections and the i-loop effective potential. Examination of the latter provides evidence for the existence of a phase boundary in parameter space between those theories with broken symmetry and those with unbroken symmetry. We extend the flow analysis near the Gaussian fixed point to Bose/Fermi theories possessing arbitrary internal symmetries. Fermionic interactions are found to decouple in parameter space. The behavior of renormalization group trajectories near the Gaussian fixed point is solely determined by the Bosonic structure of the theory. Thesis Supervisor: Kerson Huang Title: Professor