John R. Hiller, Associate Fellow

Nonperturbative Analysis of Field Theories Quantized on the Light Cone

Progress in the application of Pauli-Villars regularization included the nonperturbative solution of (3+1)-dimensional Yukawa theory in a single-fermion truncation. Three heavy scalars, including two with negative norm, were used to regulate the theory. The numerical eigenvalue problem was solved for the lowest-mass state with use of a new, indefinite-metric Lanczos algorithm. Various observables were extracted from the wave functions, including average multiplicities and average momenta of constituents, structure functions, and a form factor slope. The most recent work introduces an improved regularization scheme that uses one heavy scalar and one heavy fermion. This method has been shown to have the distinct advantage of eliminating the instantaneous fermion terms from the Hamiltonian. These terms cancel between the physical and Pauli- Villars fermions but would otherwise contribute the bulk of the nonzero Hamiltonian matrix elements. Preliminary results show much better convergence than seen with the original regularization. The better convergence is at least partly due to the absence of the instantaneous-fermion interactions.

In the work on supersymmetric theories, this researcher completed an in-depth study of the spectrum and wave functions for (2+1)-dimensional supersymmetric Yang-Mills theory. He has begun a new analysis for the theory obtained by adding a Chern-Simons term. This term provides the constituents with an effective mass without breaking the supersymmetry. The resulting theory has a spectrum that is more comparable to strong interaction physics, where the fundamental quarks and gluons do have effective masses. The researcher has also completed a study of a dimensionally reduced version of the super Yang-Mills–Chern-Simons theory, with the discovery of states in the spectrum for which the masses are nearly independent of the Yang- Mills coupling strength. Such states are expected to be found in the ongoing analysis of the full (2+1)-dimensional spectrum.