Research Abstracts Online
January 2009 - March 2010
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. Recent progress has been in the dressed-fermion sector of QED, where the problem has been solved for a two-photon truncation, and in high-resolution calculations of bound-state properties and finite-temperature effects for two-dimensional SYM theories with matter in the fundamental representation of the gauge group. 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 of the electron’s anomalous magnetic moment that includes two photons and maintains the correct chiral limit. Also, the study of temperature effects in SYM theory is being extended to three dimensions. The investigation of phi-4 theory is continuing, with computation of the effect of zero-momentum modes on convergence and vacuum structure.
Sophia Chabysheva, Research Associate
David Johnson, Graduate Student, Department of Physics, University at Albany, State University of New York, Albany, New York