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W. N. Polyzou

Publications and source records attributed to W. N. Polyzou.

At least 37 records · Page 2Linked to original sources
arXiv2014

Relativistic Formulation of Reaction Theory

A relativistic formulation of reaction theory for nuclei with a dynamics given by a unitary representations of the Poincaré group is developed. Relativistic dynamics is introduced by starting from a relativistic theory of free particles to which rotationally invariant interactions are added to the invariant mass operator. Poincaré invariance is realized by requiring that simultaneous eigenstates of the mass and spin transform as irreducible representations of the Poincaré group. A relativistic formulation of scattering theory is presented and approximations emphasizing dominant degrees of freedom that preserve unitarity, exact Poincaré invariance and exchange symmetry are discussed. A Poincaré invariant formulation of a (d,p) reaction as a three-body problem is given as an explicit example.

nucl-th↗
arXiv2014

Scattering and reflection positivity in relativistic Euclidean quantum mechanics

In this paper I discuss a formulation of relativistic few-particle scattering theory where the dynamical input is a collection of reflection-positive Euclidean covariant Green functions. This formulation of relativistic quantum mechanics has the advantage that all calculations can be performed using Euclidean variables. The construction of the Hilbert space inner product requires that the Green functions are reflection positive, which is a non-trivial constraint on the dynamics. In this paper I discuss the structure of reflection positive Green functions. I show that scattering wave operators exist when the dynamics is given by a Green function with the structure discussed in this work. Techniques for computing scattering observables in this Euclidean framework are discussed.

math-ph↗
arXiv2013

Light-Front Quantum Chromodynamics: A framework for the analysis of hadron physics

An outstanding goal of physics is to find solutions that describe hadrons in the theory of strong interactions, Quantum Chromodynamics (QCD). For this goal, the light-front Hamiltonian formulation of QCD (LFQCD) is a complementary approach to the well-established lattice gauge method. LFQCD offers access to the hadrons' nonperturbative quark and gluon amplitudes, which are directly testable in experiments at existing and future facilities. We present an overview of the promises and challenges of LFQCD in the context of unsolved issues in QCD that require broadened and accelerated investigation. We identify specific goals of this approach and address its quantifiable uncertainties.

hep-ph↗
arXiv2012

Cluster properties in Poincare invariant quantum mechanics

Using a simple model we provide a quantitative study of the size of the corrections needed to restore cluster properties to the construction of Poincare invariant dynamical models with kinematic spins, first provided by B. Bakamjian and L. H. Thomas. Our model calculations suggest that these corrections are too small to have a quantitative impact on nuclear physics observables calculated using models with meson and nucleon degrees of freedom.

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arXiv2012

Two-Nucleon Scattering without partial waves using a momentum space Argonne V18 interaction

We test the operator form of the Fourier transform of the Argonne V18 potential by computing selected scattering observables and all Wolfenstein parameters for a variety of energies. These are compared to the GW-DAC database and to partial wave calculations. We represent the interaction and transition operators as expansions in a spin-momentum basis. In this representation the Lippmann-Schwinger equation becomes a six channel integral equation in two variables. Our calculations use different numbers of spin-momentum basis elements to represent the on- and off-shell transition operators. This is because different numbers of independent spin-momentum basis elements are required to expand the on- and off-shell transition operators. The choice of on and off-shell spin-momentum basis elements is made so that the coefficients of the on-shell spin-momentum basis vectors are simply related to the corresponding off-shell coefficients.

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arXiv2012

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 Poincaré 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.

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arXiv2011

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.

nucl-th↗
arXiv2011

A momentum-space Argonne V18 interaction

This paper gives a momentum-space representation of the Argonne V18 potential as an expansion in products of spin-isospin operators with scalar coefficient functions of the momentum transfer. Two representations of the scalar coefficient functions for the strong part of the interaction are given. One is as an expansion in an orthonormal basis of rational functions and the other as an expansion in Chebyshev polynomials on different intervals. Both provide practical and efficient representations for computing the momentum-space potential that do not require integration or interpolation. Programs based on both expansions are available as supplementary material. Analytic expressions are given for the scalar coefficient functions of the Fourier transform of the electromagnetic part of the Argonne V18. A simple method for computing the partial-wave projections of these interactions from the operator expressions is also given.

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arXiv2011

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.

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arXiv2010

Poincaré Invariant Quantum Mechanics based on Euclidean Green functions

We investigate a formulation of Poincaré invariant quantum mechanics where the dynamical input is Euclidean invariant Green functions or their generating functional. We argue that within this framework it is possible to calculate scattering observables, binding energies, and perform finite Poincaré transformations without using any analytic continuation. We demonstrate, using a toy model, how matrix elements of $e^{-βH}$ in normalizable states can be used to compute transition matrix elements for energies up to 2 GeV. We discuss some open problems.

math-ph↗
arXiv2010

Mini review of Poincaré invariant quantum theory

We review the construction and applications of exactly Poincaré invariant quantum mechanical models of few-degree of freedom systems. We discuss the construction of dynamical representations of the Poincaré group on few-particle Hilbert spaces, the relation to quantum field theory, the formulation of cluster properties, and practical considerations related to the construction of realistic interactions and the solution of the dynamical equations. Selected applications illustrate the utility of this approach.

math-ph↗
arXiv2010

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.

math-ph↗
arXiv2010

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 Poincaré 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.

math-ph↗
arXiv2010

Relativistic quantum theories and neutrino oscillations

Neutrino oscillations are examined under the broad requirements of Poincaré-invariant scattering theory in an S-matrix formulation. This approach can be consistently applied to theories with either field or particle degrees of freedom. The goal of this paper is to use this general framework to identify all of the unique physical properties of this problem that lead to a simple oscillation formula. We discuss what is in principle observable, and how many factors that are important in principle end up being negligible in practice.

hep-ph↗