Forms of Relativistic Dynamics: What Are the Possibilities?

Various methods of constructing solvable few-body models are reviewed, with an emphasis on direct interactions with few degrees of freedom, as an alternative to the use of local quantum field theories. Several applications are discussed.Comment: 13 p

Model tests of cluster separability in relativistic quantum mechanics

A relativistically invariant quantum theory first advanced by Bakamjian and Thomas has proven very useful in modeling few-body systems. For three particles or more, this approach is known formally to fail the constraint of cluster separability, whereby symmetries and conservation laws that hold for a system of particles also hold for isolated subsystems. Cluster separability can be restored by means of a recursive construction using unitary transformations, but implementation is difficult in practice, and the quantitative extent to which the Bakamjian-Thomas approach violates cluster separability has never been tested. This paper provides such a test by means of a model of a scalar probe in a three-particle system for which (1) it is simple enough that there is a straightforward solution that satisfies Poincar\'e invariance and cluster separability, and (2) one can also apply the Bakamjian-Thomas approach. The difference between these calculations provides a measure of the size of the corrections from the Sokolov construction that are needed to restore cluster properties. Our estimates suggest that, in models based on nucleon degrees of freedom, the corrections that restore cluster properties are too small to effect calculations of observables.Comment: 13 pages, 15 figure

Nucleon and Pion Form Factors in Different Forms of Relativistic Quantum Mechanics

Calculations of form factors in different forms of relativistic kinematics are presented. They involve the instant, front and point forms. In the two first cases, different kinematical conditions are considered while in the latter case, both a Dirac-inspired approach and a hyperplane-based one are incorporated in our study. Numerical results are presented for the pion form factors with emphasis on both the low and high Q**2 range. A new argument is presented, explaining why some approaches do considerably much better than other ones whenonly a single-particle current is considered.Comment: To appear in the proceedings of MENU04 (Beijing, Aug. 29- Sept. 4, 2004

Covariant spectator theory of np scattering: Effective range expansions and relativistic deuteron wave functions

We present the effective range expansions for the 1S_0 and 3S_1 scattering phase shifts, and the relativistic deuteron wave functions that accompany our recent high precision fits (with chi^2/N{data} approx 1) to the 2007 world np data below 350 MeV. The wave functions are expanded in a series of analytical functions (with the correct asymptotic behavior at both large and small arguments) that can be Fourier-transformed from momentum to coordinate space and are convenient to use in any application. A fortran subroutine to compute these wave functions can be obtained from the authors.Comment: 32 pages, 14 figure