Stability of Covariant Relativistic Quantum Theory

In this paper we study the relativistic quantum mechanical interpretation of the solution of the inhomogeneous Euclidean Bethe-Salpeter equation. Our goal is to determine conditions on the input to the Euclidean Bethe-Salpeter equation so the solution can be used to construct a model Hilbert space and a dynamical unitary representation of the Poincar\'e group. We prove three theorems that relate the stability of this construction to properties of the kernel and driving term of the Bethe-Salpeter equation. The most interesting result is that the positivity of the Hilbert space norm in the non-interacting theory is not stable with respect to Euclidean covariant perturbations defined by Bethe-Salpeter kernels. The long-term goal of this work is to understand which model Euclidean Green functions preserve the underlying relativistic quantum theory of the original field theory. Understanding the constraints imposed on the Green functions by the existence of an underlying relativistic quantum theory is an important consideration for formulating field-theory motivated relativistic quantum models.Comment: 29 pages, Latex, corrected typos, added background section, improved proof of key resul

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

Electromagnetic current operators for phenomenological relativistic models

Background: Phenomenological Poincar\'e invariant quantum mechanical models can provide an efficient description of the dynamics of strongly interacting particles that is consistent with spectral and scattering observables. These models are representation dependent and in order to apply them to reactions with electromagnetic probes it is necessary to have a consistent electromagnetic current operator. Purpose: The purpose of this work is to use local gauge invariance to construct consistent strong current operators. Method: Current operators are constructed from a model Hamiltonian by replacing momentum operators in the Weyl representation by gauge covariant derivatives. Results: The construction provides a systematic method to construct explicit expressions for current operators that are consistent with relativistic models of strong interaction dynamics.Comment: 31 pages, contribution to 25-th European Conference on Few Body Problems Physics, Main