A Theorem on Light-Front Quantum Models

I give a sufficient condition for a relativistic front-form quantum mechanical model to be scattering equivalent (unitarily equivalent with the same S-matrix elements) to a relativistic front-form quantum model with an interaction-independent front-form spin.Comment: 22 pages, (TeX + PHYZZX macros

Wavelets in Field Theory

We advocate the use of Daubechies wavelets as a basis for treating a variety of problems in quantum field theory. This basis has both natural large volume and short distance cutoffs, has natural partitions of unity, and the basis functions are all related to the fixed point of a linear renormalization group equation.Comment: 42 pages, 2 figures, corrected typo

Reaction Theory

Background: Exact numerical treatments of nuclear reactions are not feasible, except for the simplest systems. Few-Body models are justified when the reactions are dominated by a small number of scattering channels. Purpose: To discuss a method for constructing few-body models from a given Hamiltonian where all of the scattering is into a chosen set of important channels and corrections due to eliminated channels can be systematically computed. Method:The method uses cluster decompositions and spectral expansions of proper subsystems to control the absolutely continuous spectrum of the many-body Hamiltonian. Results: The result is a decomposition of the exact Hamiltonian into two parts, one that satisfies an optical theorem in a chosen set of important channels and one that satisfies an optical theorem in the complementary channels. When the reaction has a small number of dominant channels, the dominant channel part of the Hamiltonian is an effective few-body Hamiltonian. The decomposition has the property that the scattering wave functions from the dominant channel Hamiltonian agree with the exact scattering wave functions up to, but not including, $N$-body correlations.Comment: 29 page