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

Relativistic Quantum Mechanics - Particle Production and Cluster Properties

This paper constructs relativistic quantum mechanical models of particles satisfying cluster properties and the spectral condition which do not conserve particle number. The treatment of particle production is limited to systems with a bounded number of bare-particle degrees of freedom. The focus of this paper is about the realization of cluster properties in these theories.Comment: 36 pages, Late

Comment on the equivalence of Bakamjian-Thomas mass operators in different forms of dynamics

We discuss the scattering equivalence of the generalized Bakamjian-Thomas construction of dynamical representations of the Poincar\'e group in all of Dirac's forms of dynamics. The equivalence was established by Sokolov in the context of proving that the equivalence holds for models that satisfy cluster separability. The generalized Bakamjian Thomas construction is used in most applications, even though it only satisfies cluster properties for systems of less than four particles. Different forms of dynamics are related by unitary transformations that remove interactions from some infinitesimal generators and introduce them to other generators. These unitary transformation must be interaction dependent, because they can be applied to a non-interacting generator and produce an interacting generator. This suggests that these transformations can generate complex many-body forces when used in many-body problems. It turns out that this is not the case. In all cases of interest the result of applying the unitary scattering equivalence results in representations that have simple relations, even though the unitary transformations are dynamical. This applies to many-body models as well as models with particle production. In all cases no new many-body operators are generated by the unitary scattering equivalences relating the different forms of dynamics. This makes it clear that the various calculations used in applications that emphasize one form of the dynamics over another are equivalent. Furthermore, explicit representations of the equivalent dynamical models in any form of dynamics are easily constructed. Where differences do appear is when electromagnetic probes are treated in the one-photon exchange approximation. This approximation is different in each of Dirac's forms of dynamics.Comment: 6 pages, no figure

Poincar\'e Invariant Three-Body Scattering at Intermediate Energies

The relativistic Faddeev equation for three-nucleon scattering is formulated in momentum space and directly solved in terms of momentum vectors without employing a partial wave decomposition. The equation is solved through Pad\'e summation, and the numerical feasibility and stability of the solution is demonstrated. Relativistic invariance is achieved by constructing a dynamical unitary representation of the Poincar\'e group on the three-nucleon Hilbert space. Based on a Malfliet-Tjon type interaction, observables for elastic and break-up scattering are calculated for projectile energies in the intermediate energy range up to 2 GeV, and compared to their nonrelativistic counterparts. The convergence of the multiple scattering series is investigated as a function of the projectile energy in different scattering observables and configurations. Approximations to the two-body interaction embedded in the three-particle space are compared to the exact treatment.Comment: 16 pages, 13 figure

Constraints of cluster separability and covariance on current operators

Realistic models of hadronic systems should be defined by a dynamical unitary representation of the Poincare group that is also consistent with cluster properties and a spectral condition. All three of these requirements constrain the structure of the interactions. These conditions can be satisfied in light-front quantum mechanics, maintaining the advantage of having a kinematic subgroup of boosts and translations tangent to a light front. The most straightforward construction of dynamical unitary representations of the Poincare group due to Bakamjian and Thomas fails to satisfy the cluster condition for more than two particles. Cluster properties can be restored, at significant computational expense, using a recursive method due to Sokolov. In this work we report on an investigation of the size of the corrections needed to restore cluster properties in Bakamjian-Thomas models with a light-front kinematic symmetry. Our results suggest that for models based on nucleon and meson degrees of freedom these corrections are too small to be experimentally observed.Comment: Contribution to Light Cone 2011, Dallas TX, 4 pages, 2 figure

Relativity and the low energy nd Ay puzzle

We solve the Faddeev equation in an exactly Poincare invariant formulation of the three-nucleon problem. The dynamical input is a relativistic nucleon-nucleon interaction that is exactly on-shell equivalent to the high precision CDBonn NN interaction. S-matrix cluster properties dictate how the two-body dynamics is embedded in the three-nucleon mass operator. We find that for neutron laboratory energies above 20 MeV relativistic effects on Ay are negligible. For energies below 20 MeV dynamical effects lower the nucleon analyzing power maximum slightly by 2% and Wigner rotations lower it further up to 10 % increasing thus disagreement between data and theory. This indicates that three-nucleon forces must provide an even larger increase of the Ay maximum than expected up to now.Comment: 29 pages, 2 ps figure

Poincare Invariant Three-Body Scattering

Relativistic Faddeev equations for three-body scattering are solved at arbitrary energies in terms of momentum vectors without employing a partial wave decomposition. Relativistic invariance is incorporated withing the framework of Poincar\'e invariant quantum mechanics. Based on a Malfliet-Tjon interaction, observables for elastic and breakup scattering are calculated and compared to non-relativistic ones.Comment: 4 pages, 2 figures. Proceedings of the workshop "Critical Stability of Few-Body Quantum Systems" 200

Quantitative Relativistic Effects in the Three-Nucleon Problem

The quantitative impact of the requirement of relativistic invariance in the three-nucleon problem is examined within the framework of Poincar\'e invariant quantum mechanics. In the case of the bound state, and for a wide variety of model implementations and reasonable interactions, most of the quantitative effects come from kinematic factors that can easily be incorporated within a non-relativistic momentum-space three-body code.Comment: 15 pages, 15 figure

First Order Relativistic Three-Body Scattering

Relativistic Faddeev equations for three-body scattering at arbitrary energies are formulated in momentum space and in first order in the two-body transition-operator directly solved in terms of momentum vectors without employing a partial wave decomposition. Relativistic invariance is incorporated within the framework of Poincare invariant quantum mechanics, and presented in some detail. Based on a Malfliet-Tjon type interaction, observables for elastic and break-up scattering are calculated up to projectile energies of 1 GeV. The influence of kinematic and dynamic relativistic effects on those observables is systematically studied. Approximations to the two-body interaction embedded in the three-particle space are compared to the exact treatment.Comment: 26 pages, 13 figure

Three-nucleon force in relativistic three-nucleon Faddeev calculations

We extend our formulation of relativistic three-nucleon Faddeev equations to include both pairwise interactions and a three-nucleon force. Exact Poincare invariance is realized by adding interactions to the mass Casimir operator (rest Hamiltonian) of the non-interacting system without changing the spin Casimir operator. This is achieved by using interactions defined by rotationally invariant kernels that are functions of internal momentum variables and single-particle spins that undergo identical Wigner rotations. To solve the resulting equations one needs matrix elements of the three-nucleon force with these properties in a momentum-space partial-wave basis. We present two methods to calculate matrix elements of three-nucleon forces with these properties. For a number of examples we show that at higher energies, where effects of relativity and of three-nucleon forces are non-negligible, a consistent treatment of both is required to properly analyze the data.Comment: 49 pages, 18 figure