Considerable interest has developed in the use of light-cone quantization in the construction of solvable bound-state problems for strongly interacting theories of elementary particles. The coordinates used are based on the choice of t + z/c as the time coordinate, where t is the ordinary time, z is any Cartesian spatial coordinate, and c is the speed of light. A variety of quantum field theories have been analyzed in this way. The aim of these investigations is to develop methods that will permit a qualitative, or even quantitative, understanding of bound states in quantum chromodynamics (QCD). Because QCD is the leading candidate for the theory of the strong interactions, an understanding of its bound states is vital. Comparison with the experimentally determined properties of hadrons can then be made as important low-energy tests of the theory.
Cosmin Deciu, Graduate Student Researcher
Ajaya Ghimire, Graduate Student Researcher
99/47 |
"Application of Pauli-Villars Regularization and Discretized Light-Cone Quantization to a (3 + 1)-Dimensional Model," S.J. Brodsky, J.R. Hiller, and G. McCartor, Physical Review D, 60, p. 054506 (1999). |
99/140 |
"Pauli-Villars Regularization in DLCQ," J.R. Hiller, in New Directions in Quantum Chromodynamics, edited by C.-R. Ji and D.-P. Min (American Institute of Physics, 1999) p. 252. |
99/160 |
"On the Use of Discrete Light-Cone Quantization to Compute Form Factors," J.R. Hiller, University of Minnesota Supercomputing Institute Research Report UMSI 99/160, September 1999. |
99/230 |
"The Mass Spectrum of N = 1 SYM2+1 at Strong Coupling," P. Haney, J.R. Hiller, O. Lunin, S.S. Pinsky, and U. Trittmann, University of Minnesota Supercomputing Institute Research Report UMSI 99/230, December 1999. |
Because of the complexity of QCD, it is preferable to begin with other theories when developing
nonperturbative techniques. This work began with scalar theories, diagonalized with use of the
Lanczos algorithm. To bring the work closer to QCD, quantum electrodynamics (QED) was considered.
Here, a nearly complete formulation of regularization and renormalization was developed for a
calculation of the anomalous moment of the electron. A diagrammatic analysis guided construction
of counterterms that were then fixed by nonperturbative renormalization conditions.
As an alternative approach to regularization and renormalization, Pauli-Villars techniques are being
investigated in simple scalar-fermion models. Analytic work on a heavy source model produced a
soluble case, and a numerical approximation has been successfully tested and extended to include a
dynamical source. Current work deals with a single-fermion truncation to Yukawa theory. The next step
is a two-fermion truncation where true bound states, as opposed to a fermion dressed by a cloud of
bosons, can be studied.
Code developed for the single-fermion Yukawa problem is directly applicable to the electron
anomalous moment calculation, with changes in expressions for interaction terms of the Hamiltonian
and in the boson helicities. Renormalization conditions that fix bare parameters require
approximation of scattering processes, something of interest in its own right. A field-theoretic
form of the Lanczos-based Haydock recursion method has been developed and will be tested.
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