Equivalent Hamiltonians

I give a characterization of the conditions for two Hamiltonians to be equivalent, discuss the construction of the operators that relate equivalent Hamiltonians, and introduce variational methods that can select Hamiltonians with desirable features from the space of equivalent Hamiltonians.Comment: 15 page

The light-front vacuum and dynamics

I give a quantum theoretical description of kinematically invariant vacuua on the algebra of free fields restricted to a light front and discuss the relation between the light-front Hamiltonian, P-, the vacuum, and Poincare invariance. This provides a quantum theoretical description of zero modes.Comment: 5 pages, Talk at Light-Cone 200

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

Relativistic Quantum Dynamics of Many-Body Systems

Relativistic quantum dynamics requires a unitary representation of the Poincare group on the Hilbert space of states. The dynamics of many-body systems must satisfy cluster separability requirements. In this paper we formulate an abstract framework of four dimensional Euclidean Green functions that can be used to construct relativistic quantum dynamics of N-particle systems consistent with these requirements. This approach should be useful in bridging the gap between few-body dynamics based on phenomenological mass operators and on quantum field theory.Comment: Latex, 9 Pages, Submitted to World Scientific - 50 Years of Quantum Many-Body Theory - A Conference in Honor of the 65-th Birthdays of John W. Clark, Alpo J. Kallio, Manfred L. Ristig, and Sergio Rosat

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