Final Scientific Report for ER41087

Abstract

The primary focus of the work was the development of methods for the nonperturbative solution of quantum chromodynamics (QCD) in a form that yields wave functions for the eigenstates, from which hadronic properties can be computed. The principal approach was to use a light-front Hamiltonian formulation. In light-front coordinates, t+z/c plays the role of time, with t the ordinary time, z a space direction, and c the speed of light. This leads to a relativistic formulation that retains useful characteristics of nonrelativistic treatments. A bound state of many constituents can be represented by wave functions that define probabilities for each possible arrangement of internal momenta. These functions satisfy integral equations that can be approximated numerically to yield a matrix representation. The matrix problem can be solved by iterative methods. The approximate wave functions can then be used to compute properties of the bound state. Methods have been developed for model theories and gauge theories, including quantum electrodynamics and theories that are supersymmetric. The work has required the development of new numerical algorithms and computer codes for singular integral equations and eigenvalue problems. A key aspect of the work is the construction of practical procedures for nonperturbative regularization and renormalization. Two methods of regularization have been studied. One is the addition of heavy Pauli--Villars (PV) particles to the Lagrangian, with their metrics and couplings tuned to provide the necessary cancellations in the regularization. The other method of regularization is the addition of supersymmetric partners, to extend a theory to a supersymmetric form. The supersymmetric theories were solved by the supersymmetric discrete light-cone quantization (SDLCQ) method. The most significant accomplishments of the project were the SDLCQ calculation of direct evidence for a Maldacena duality conjecture, construction of a practical light-front quantization for QED in an arbitrary covariant gauge, and invention of the light-front coupled-cluster method, designed to eliminate the need for Fock-space truncations.