Truncated Fock Space Research Articles

Light-front QCD. III. Coupling constant renormalization.

In this third part in a series of papers on light-front QCD, we continue the study of regularization and renormalization in old-fashioned perturbative light-front formalism. We calculate lowest order radiative corrections to the quark-gluon coupling constant in light-front QCD. An attempt is made to understand the origin of antiscreening in a formulation of QCD with only physical degrees of freedom in terms of contributions from distinct Fock space sectors. The relevance of our results to bound state calculations in QCD with a truncated Fock space are discussed.

Basis Function Calculations for the Massive Schwinger Model in the Light-Front Tamm-Dancoff Approximation

We use light-front field theory to study the massive Schwinger model. After making a Tamm-Dancoff truncation of Fock space so that no more than four particles are allowed in any state, the coupled light-front Tamm-Dancoff integral equations for charge zero states are solved by expanding the two-particle and four-particle amplitudes in a finite basis, thereby converting the original equations into a simple matrix equation. By retaining the four-particle sector we are able to study both the lowest energy boson of the theory and the first excited state, which for massless fermions is a scattering state of two ground state bosons. Known results for the massless Schwinger model are accurately reproduced with reasonably small bases, and existing numerical results for the massive model are reproduced and improved. The rich physics of the Schwinger model is used to elucidate several simple problems in the use of basis functions to solve Hamiltonian field theories.

Compton scattering in the light-cone Tamm-Dancoff approximation.

The Tamm-Dancoff approximation is used to study Compton scattering in light-cone-quantized QED (D. Mustaki, S. Pinsky, J. Shigemitsu, and K. G. Wilson) The charge-one sector is considered in a two-particle truncated Fock space. The problem is exactly solvable and it is shown that the internal photon propagator develops a singularity similar to the one reported in the light-cone calculation of positronium (M. Krautg\"artner, H. C. Pauli, and F. W\"olz). This singularity depends on the external energy and therefore cannot be removed by the conventional counterterms.