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Research Abstracts Online
January 2008 - March 2009

University of Minnesota Duluth
Swenson College of Science and Engineering
Department of Physics

PI: John R. Hiller, Fellow

Nonperturbative Analysis of Field Theories Quantized on the Light Cone

The interactions between fundamental particles can be described with quantum field theories, and the use of light-cone coordinates can be advantageous in determining the properties of the bound states that these particles can form. The state of the system can then be expanded in a basis of momentum eigenstates, with wave functions as the coefficients in the expansion. The wave functions satisfy a coupled system of integral equations that almost always require numerical techniques for their solution. Within the integrals there are infinities that must be regulated in some way in order to properly define the given theory.

This project considers two methods for the removal of such infinities: Pauli-Villars regularization, which requires the introduction of unphysical massive particles, and supersymmetry. These researchers have applied these methods to various field theories, in particular Yukawa theory, quantum electrodynamics (QED), super Yang-Mills (SYM) theory, and phi-4 theory, and are continuing to explore their use with the ultimate goal of applying them to quantum chromodynamics (QCD), the theory of the strong interactions that determine the properties of mesons and baryons. Current work on Yukawa theory considers states with two fermionic constituents, and will provide a starting point for a QCD-based meson model calculation. The researchers are performing a QED calculation that includes two photons, and the study of temperature effects in SYM theory is being extended to three dimensions. Investigation of phi-4 theory explores the practical introduction of zero-momentum modes to improve convergence and study vacuum structure.

Group Members

David Johnson, Graduate Student, Department of Physics, University at Albany, State University of New York, Albany, New York
Sophia Tchabycheva, Graduate Student, Department of Physics, Southern Methodist University, Dallas, Texas