arXiv subjects
Publications and source records attributed to W. N. Polyzou.
We discuss preliminary work on a formulation of relativistic quantum mechanics that uses reflection-positive Euclidean Green functions or their generating functionals as phenomenological input. We discuss the construction of a Poincare invariant S-matrix from matrix element of exp(- βH).
We investigate exchange current contributions to elastic electron-deuteron scattering using exactly Poincaré invariant quantum mechanics with a null-plane kinematic symmetry. Our model exchange current is motivated by one-pion-exchange physics. Exact current conservation and current covariance are satisfied by using this current to compute a linearly independent set of current matrix elements. The remaining current matrix elements are generated from the independent matrix elements using the covariance and current conservation constraints. The presence of the exchange current increases the sensitivity to the choice of independent current matrix elements. Two choices of independent matrix elements that have distinct motivations lead to a good description of all of the elastic scattering observables for momentum transfers below 8 (GeV)$^2$.
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 Poincaré invariant quantum mechanics. Based on a Malfliet-Tjon interaction, observables for elastic and breakup scattering are calculated and compared to non-relativistic ones.
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 Padé summation, and the numerical feasibility and stability of the solution is demonstrated. Relativistic invariance is achieved by constructing a dynamical unitary representation of the Poincaré 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.
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.
The relativistic three-nucleon problem is formulated by constructing a dynamical unitary representation of the Poincaré group on the three-nucleon Hilbert space. Two-body interactions are included that preserve the Poincaré symmetry, lead to the same invariant two-body S-matrix as the corresponding non-relativistic problem, and result in a three-body S-matrix satisfying cluster properties. The resulting Faddeev equations are solved by direct integration, without partial waves for both elastic and breakup reactions at laboratory energies up to 2 Gev.
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. Relativistic invariance is achieved by constructing a dynamical unitary representation of the Poincaré group on the three-nucleon Hilbert space. The exclusive breakup reaction at 508 MeV is calculated based on a Malfliet-Tjon type of two-body interaction and the cross sections are compared to measured cross sections at this energy. We find that the magnitude of the relativistic effects can be quite large and depends on the configurations considered. In spite of the simple nature of the model interaction, the experimental cross sections are in surprisingly good agreement with the predictions of the relativistic calculations. We also find that although for specific configurations the multiple scattering series converges rapidly, this is in general not the case.
Relativistic Faddeev equations for three-body scattering at arbitrary energies are solved in first order in the two-body transition operator in terms of momentum vectors without employing a partial wave decomposition. Relativistic invariance is incorporated within the framework of Poincar{é} invariant quantum mechanics. Based on a Malfliet-Tjon type interaction, observables for elastic and breakup scattering are calculated and compared to the nonrelativistic ones.
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.
In this paper we discuss the use of wavelet bases to solve the relativistic three-body problem. Wavelet bases can be used to transform momentum-space scattering integral equations into an approximate system of linear equations with a sparse matrix. This has the potential to reduce the size of realistic three-body calculations with minimal loss of accuracy. The wavelet method leads to a clean, interaction independent treatment of the scattering singularities which does not require any subtractions.
The quantitative impact of the requirement of relativistic invariance in the three-nucleon problem is examined within the framework of Poincaré 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.
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.
Experimental data of the pion charge form factor are well represented by Poincaré invariant constituent-quark phenomenology depending on two parameters, a confinement scale and an effective constituent--quark mass. Pion states are represented by eigenfunctions of mass and spin operators and of the light-front momenta. An effective current density is generated by the dynamics from a null-plane impulse current density. A simple shape of the wave function depending only on the confinement scale is sufficient.
The use of orthonormal wavelet basis functions for solving singular integral scattering equations is investigated. It is shown that these basis functions lead to sparse matrix equations which can be solved by iterative techniques. The scaling properties of wavelets are used to derive an efficient method for evaluating the singular integrals. The accuracy and efficiency of the wavelet transforms is demonstrated by solving the two-body T-matrix equation without partial wave projection. The resulting matrix equation which is characteristic of multiparticle integral scattering equations is found to provide an efficient method for obtaining accurate approximate solutions to the integral equation. These results indicate that wavelet transforms may provide a useful tool for studying few-body systems.
In this paper scattering equivalences are used to simplify current operators in constituent quark models. The simplicity of the method is illustrated by applying it to a relativistic constituent quark model that fits the meson mass spectrum. This model requires a non-trivial constituent quark current operator to fit the pion form factor data. A model with a different confining interaction, that has the identical spectrum and can reproduce the measured pion form factor using only point-like constituent quark impulse currents is constructed. Both the original and transformed models are relativistic direct-interaction models with a light-front kinematic subgroup.
Wavelets are a useful basis for constructing solutions of the integral and differential equations of scattering theory. Wavelet bases efficiently represent functions with smooth structures on different scales, and the matrix representation of operators in a wavelet basis are well-approximated by sparse matrices. The basis functions are related to solutions of a linear renormalization group equation, and the basis functions have structure on all scales. Numerical methods based on this renormalization group equation are discussed. These methods lead to accurate and efficient numerical approximations to the scattering equations. These notes provide a detailed introduction to the subject that focuses on numerical methods. We plan to provide periodic updates to these notes.
I formulate a class of relativistic quantum mechanical models that satisfy the cluster property and allow particle production. The models have a finite number of bare-particle degrees of freedom. The class of models include relativistic isobar models and the relativistic Lee model. I discuss elements of the construction that may be relevant to treat the general case of an infinite number of degrees of freedom.
We demonstrate that wavelet bases have features that make them advantageous for solving momentum-space scattering integral equations. Using the example of two nucleons interacting with the Malfliet-Tjon V interaction, we show it is possible to reduce the size of the matrix representation of the Lippmann-Scwhinger equation by 96% with a loss of accuracy of only a few parts in a million. We also demonstrate that wavelet methods provide an accurate means for treating the singularities that appear in the scattering integral equations.