## Research Abstracts Online

January 2010 - March 2011

Main TOC

### 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

Quantum field theories are used to describe interactions between fundamental particles. In determining the properties of the bound states that these particles can form, the use of light-cone coordinates, with *t+z/c* playing the role of time, can be advantageous. 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 which must be regulated in some way in order to properly define the given theory.

In this project, these researchers consider two methods: Pauli-Villars regularization, which requires the introduction of unphysical massive particles, and supersymmetry. These methods have been applied to various field theories, in particular Yukawa theory, quantum electrodynamics (QED), super Yang-Mills (SYM) theory, and phi-4 theory, and continue to be explored, 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 and dressed-photon sectors of QED, where the problem has been solved for a two-photon truncation of the electron state and an electron-positron truncation of the photon state, 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. A QED calculation of the electron's anomalous magnetic moment, that includes two photons and an electron-positron pair, is in progress. The study of finite-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.

### Group Members

Sophia Chabysheva, Research Associate

David Johnson, Graduate Student