7 research outputs found
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, -body correlations.Comment: 29 page