Comparing relativistic three-body wave equations with non-relativistic bound-states results in scalar QFT

2020 ◽  
Vol 59 (5) ◽  
pp. 1475-1489 ◽  
Author(s):  
Mohsen Emami-Razavi
Keyword(s):  
Bound States ◽  
Wave Equations ◽  
Body Wave ◽  
Three Body ◽  
Relativistic Bound States

scholarly journals Electromagnetic transition form factors of baryons in a relativistic Faddeev approach

2018 ◽  
Vol 181 ◽  
pp. 01013 ◽  
Author(s):  
Reinhard Alkofer ◽  
Christian S. Fischer ◽  
Hèlios Sanchis-Alepuz
Keyword(s):  
Ground State ◽  
Bound States ◽  
Body Wave ◽  
Form Factors ◽  
Wave Functions ◽  
Electromagnetic Form Factors ◽  
Transition Form ◽  
Electromagnetic Transition ◽  
Three Body ◽  
Gluon Interaction

The covariant Faddeev approach which describes baryons as relativistic three-quark bound states and is based on the Dyson-Schwinger and Bethe-Salpeter equations of QCD is briefly reviewed. All elements, including especially the baryons’ three-body-wave-functions, the quark propagators and the dressed quark-photon vertex, are calculated from a well-established approximation for the quark-gluon interaction. Selected previous results of this approach for the spectrum and elastic electromagnetic form factors of ground-state baryons and resonances are reported. The main focus of this talk is a presentation and discussion of results from a recent investigation of the electromagnetic transition form factors between ground-state octet and decuplet baryons as well as the octet-only Σ0 to Λ transition.

Variational wave equations for relativistic few-body systems in QFT

2006 ◽  
Vol 84 (6-7) ◽  
pp. 625-632 ◽  
Author(s):  
J W Darewych
Keyword(s):  
Field Theory ◽  
Bound States ◽  
Wave Equations ◽  
Body Wave ◽  
Hamiltonian Formalism ◽  
Approximate Solutions ◽  
Quantum Field ◽  
Fermion Fields ◽  
Variational Wave ◽  
03.65 Ge

The variational method in a reformulated Hamiltonian formalism of quantum field theory is used to derive relativistic few-body wave equations for scalar and Fermion fields. Analytic and approximate solutions of some two-body bound states are presented.PACS Nos.: 03.65.Pm, 03.65.Ge, 03.70.+k, 11.10.Ef, 11.10.St, 11.15.Tk, 36.10.Dr

ENERGY LEVELS OF QUARKONIA IN POTENTIAL MODELS

1987 ◽  
Vol 02 (06) ◽  
pp. 1669-1705 ◽  
Author(s):  
D.B. LICHTENBERG
Keyword(s):  
Quantum Chromodynamics ◽  
Heavy Quark ◽  
Bound States ◽  
Wave Equations ◽  
Body Wave ◽  
Energy Levels ◽  
Spin Dependence ◽  
Potential Models ◽  
Potential Approach ◽  
The Subject

We review the subject of the energy levels of light and heavy quark-antiquark bound states in potential models, with emphasis on potentials which are motivated from quantum chromodynamics. In addition to pointing out the successes of potential models, we discuss problems with the potential approach, including uncertainties in the form of the potential, its spin dependence, its transformation properties, and its nondiagonal terms. We consider two-body wave equations with both nonrelativistic and relativistic kinematics, pointing out that in the latter case, a wide variety of different wave equations have been used in the literature.

Quantum Numbers of Eigenstates of Generalized de Broglie-Bargmann- Wigner Equations for Fermions with Partonic Substructure

2003 ◽  
Vol 58 (1) ◽  
pp. 1-12 ◽  
Author(s):  
H. Stumpf
Keyword(s):  
Angular Momentum ◽  
Integral Equations ◽  
Bound States ◽  
Solution Space ◽  
Many Body ◽  
Quantum Numbers ◽  
Relevant Group ◽  
Three Body ◽  
Relativistic Bound States ◽  
Fusion Theory

Generalized de Broglie-Bargmann-Wigner (BBW) equations are relativistically invariant quantum mechanical many body equations with nontrivial interaction, selfregularization and probability interpretation. Owing to these properties these equations are a suitable means for describing relativistic bound states of fermions. In accordance with de Broglie’s fusion theory and modern assumptions about the partonic substructure of elementary fermions, i.e., leptons and quarks, the three-body generalized BBW-equations are investigated. The transformation properties and quantum numbers of the three-parton equations under the relevant group actions are elaborated in detail. Section 3 deals with the action of the isospin group SU(2), a U(1) global gauge group for the fermion number, the hypercharge and charge generators. The resulting quantum numbers of the composite partonic systems can be adapted to those of the phenomenological particles to be described. The space-time transformations and in particular rotations generated by angular momentum operators are considered in Section 4. Based on the compatibility of the BBW-equations and the group theoretical constraints, in Sect. 5 integral equations are formulated in a representation with diagonal energy and total angular momentum variables. The paper provides new insight into the solution space and quantum labels of resulting integral equations for three parton states and prepares the ground for representing leptons and quarks as composite systems.

scholarly journals RELATIVISTIC BOUND STATES IN THE PRESENCE OF SPHERICALLY RING-SHAPED q-DEFORMED WOODS–SAXON POTENTIAL WITH ARBITRARY l-STATES

2013 ◽  
Vol 22 (03) ◽  
pp. 1350015 ◽  
Author(s):  
SAMEER M. IKHDAIR ◽  
MAJID HAMZAVI ◽  
A. A. RAJABI
Keyword(s):  
Bound States ◽  
Wave Equations ◽  
Jacobi Polynomials ◽  
Energy Eigenvalue ◽  
Bound State ◽  
Wave Functions ◽  
Potential Term ◽  
Component Wave ◽  
Relativistic Bound States ◽  
Potential Parameters

Approximate bound-state solutions of the Dirac equation with q-deformed Woods–Saxon (WS) plus a new generalized ring-shaped (RS) potential are obtained for any arbitrary l-state. The energy eigenvalue equation and corresponding two-component wave functions are calculated by solving the radial and angular wave equations within a shortcut of the Nikiforov–Uvarov (NU) method. The solutions of the radial and polar angular parts of the wave function are expressed in terms of the Jacobi polynomials. A new approximation being expressed in terms of the potential parameters is carried out to deal with the strong singular centrifugal potential term l(l+1)r-2. Under some limitations, we can obtain solution for the RS Hulthén potential and the standard usual spherical WS potential (q = 1).

scholarly journals On relativistic entanglement and localization of particles and on their comparison with the nonrelativistic theory

2014 ◽  
Vol 29 (29) ◽  
pp. 1450163 ◽  
Author(s):  
Horace W. Crater ◽  
Luca Lusanna
Keyword(s):  
Bound States ◽  
Clock Synchronization ◽  
Center Of Mass ◽  
Particle Beams ◽  
Open Problems ◽  
Inertial Frames ◽  
Classical Trajectories ◽  
Particle Localization ◽  
Relativistic Bound States ◽  
Classical And Quantum Mechanics

We make a critical comparison of relativistic and nonrelativistic classical and quantum mechanics of particles in inertial frames as well of the open problems in particle localization at both levels. The solution of the problems of the relativistic center-of-mass, of the clock synchronization convention needed to define relativistic 3-spaces and of the elimination of the relative times in the relativistic bound states leads to a description with a decoupled nonlocal (nonmeasurable) relativistic center-of-mass and with only relative variables for the particles (single particle subsystems do not exist). We analyze the implications for entanglement of this relativistic spatial nonseparability not existing in nonrelativistic entanglement. Then, we try to reconcile the two visions showing that also at the nonrelativistic level in real experiments only relative variables are measured with their directions determined by the effective mean classical trajectories of particle beams present in the experiment. The existing results about the nonrelativistic and relativistic localization of particles and atoms support the view that detectors only identify effective particles following this type of trajectories: these objects are the phenomenological emergent aspect of the notion of particle defined by means of the Fock spaces of quantum field theory.

A COMPLETE VARIATIONAL WAVE FUNCTION FOR THE GROUND STATE OF 3H AND 3He

1966 ◽  
Vol 44 (9) ◽  
pp. 2095-2110 ◽  
Author(s):  
Marcel Banville ◽  
P. D. Kunz
Keyword(s):  
Wave Function ◽  
Coordinate System ◽  
Body Wave ◽  
Center Of Mass ◽  
Minimum Energy ◽  
Equal Mass ◽  
Radial Coordinate ◽  
Orthogonal Functions ◽  
Gaussian Shape ◽  
Three Body

The three-body wave function for particles of equal mass is expanded in a systematic way by making use of a hyperspherical coordinate system. Apart from the center-of-mass coordinates, three of the variables are the usual Euler angles describing the orientation of the plane defined by the three particles. The other three variables, which describe the shape of the triangle, are represented in terms of a radial coordinate and two angular coordinates. The kinetic energy for these last three coordinates is separable and allows one to expand the three-body wave function in a complete set of orthogonal functions based upon the angular variables. The particular symmetry of the internal part of the wave function under permutations of the three particles is easily represented in terms of the set of functions for one of the angular variables. By choosing a particular set of radial functions one can then obtain the upper limit on the binding energy for the three-body system through the Rayleigh–Ritz variational procedure. The advantage of this particular coordinate system is that all but a few of the variational parameters occur linearly in the wave function, and the minimum energy can be obtained by diagonalizing a small number of the energy matrices. The method is applied to find the lower limit to a standard spin-independent potential of Gaussian shape.

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