How to obtain a covariant Breit type equation from relativistic constraint theory

Mourad, J.; Sazdjian, H.

doi:10.1088/0954-3899/21/3/004

Cited by 22 publications

(28 citation statements)

References 35 publications

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“…Using identities in the beginning of this section we nd that the dierence equation becomes conrming the expectation that these momenta remain orthogonal after the interaction is introduced. This result has also been obtained recently by Mourad and Sazdjian [18] who emphasize that this would ensure the Poincaire' invariance of the theory. They further point out that the c.m.…”

Section: A General Interaction For Two-body Dirac Equationssupporting

confidence: 84%

“…energy dependence of the potential in the \main equation" (our Eq. (4.10)) ensures the global charge conjugation symmetry [18] of the system, a feature that is missing from the original Breit equation. In summary, the constraint equations imply covariant Breit-like equations of a certain form (4.10) whose wave function also satises the constraint equation We point out nally that the application of the constraint equations to electromagnetic interactions does not involve the term 1 r 2 rappearing in the Breit interaction Eq.…”

Section: A General Interaction For Two-body Dirac Equationsmentioning

confidence: 99%

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Singularity-Free Breit Equation From Constraint Two-Body Dirac Equations

Crater¹,

Wong

1996

Int. J. Mod. Phys. E

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We examine the relation between two approaches to the quantum relativistic two-body problem: (1) the Breit equation, and (2) the two-body Dirac equations derived from constraint dynamics. In applications to quantum electrodynamics, the former equation becomes pathological if certain interaction terms are not treated as perturbations. The diculty comes from singularities which appear at nite separations r in the reduced set of coupled equations for attractive potentials even when the potentials themselves are not singular there. They are known to give rise to unphysical bound states and resonances.In contrast, the two-body Dirac equations of constraint dynamics do not have these pathologies in many nonperturbative treatments. To understand these 1 marked dierences we rst express these contraint equations, which h a v e a n \external potential" form similar to coupled one-body Dirac equations, in a hyperbolic form. These coupled equations are then re-cast into two equivalent equations: (1) a covariant Breit-like equation with potentials that are exponential functions of certain \generator" functions, and (2) a covariant orthogonality constraint on the relative momentum. This reduction enables us to show in a transparent w a y that nite-r singularities do not appear as long as the the exponential structure is not tampered with and the exponential generators of the interaction are themselves nonsingular for nite r. These Dirac or Breit equations, free of the structural singularities which plague the usual Breit equation, can then be used safely under all circumstances, encompassing numerous applications in the elds of particle, nuclear, and atomic physics which i n v olve highly relativistic and strong binding congurations.2

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Section: A General Interaction For Two-body Dirac Equationssupporting

confidence: 84%

Section: A General Interaction For Two-body Dirac Equationsmentioning

confidence: 99%

Singularity-Free Breit Equation From Constraint Two-Body Dirac Equations

Crater¹,

Wong

1996

Int. J. Mod. Phys. E

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“…frame. In this paper we use a recently developed rearrangement of these equations [53] (similar to that first presented in [54]) that provides us with ones simpler to solve but physically equivalent The resulting local Schrödinger-like equation depending on the four-component spinor φ + ≡ ψ 1 + ψ 4 takes the general c.m. form However, the detailed form of Φ for φ + results from their elimination through the Pauli reduction procedure.…”

Section: The Two-body Dirac Equations Of Constraint Dynamicsmentioning

confidence: 99%

Relativistic calculation of the meson spectrum: A fully covariant treatment versus standard treatments

2004

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A large number of treatments of the meson spectrum have been tried that consider mesons as quark -anti quark bound states. Recently, we used relativistic quantum "constraint" mechanics to introduce a fully covariant treatment defined by two coupled Dirac equations. For field-theoretic interactions, this procedure functions as a "quantum mechanical transform of Bethe-Salpeter equation". Here, we test its spectral fits against those provided by an assortment of models: Wisconsin model, Iowa State model, Brayshaw model, and the popular semi-relativistic treatment of Godfrey and Isgur. We find that the fit provided by the two-body Dirac model for the entire meson spectrum competes with the best fits to partial spectra provided by the others and does so with the smallest number of interaction functions without additional cutoff parameters necessary to make other approaches numerically tractable. We discuss the distinguishing features of our model that may account for the relative overall success of its fits. Note especially that in our approach for QCD, the resulting pion mass and associated Goldstone behavior depend sensitively on the preservation of relativistic couplings that are crucial for its success when solved nonperturbatively for the analogous two-body bound-states of QED. * hcrater@utsi.edu

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“…Following by the constraint formalism [10,11,12,13,14,15] it is described by the pair of covariant Dirac equations…”

Section: Appendix Covariant Form Of 2bdementioning

confidence: 99%

“…The full collection is available at http://www.emis.de/journals/SIGMA/symmetry2007.html 1 Here we mention three formulations of 2BDE approach. One of them [4,5,6,7] is built as a generalization of the Breit equation [8,9], two other, [10,11,12] and [13,14,15], originate from Dirac constraint theory. in a compact form and then to impose constraints for general potential which considerably simplify the equations.…”

Section: Introductionmentioning

confidence: 99%

Solvable Two-Body Dirac Equation as a Potential Model of Light Mesons

Duviryak¹

2008

SIGMA

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Abstract. The two-body Dirac equation with general local potential is reduced to the pair of ordinary second-order differential equations for radial components of a wave function. The class of linear + Coulomb potentials with complicated spin-angular structure is found, for which the equation is exactly solvable. On this ground a relativistic potential model of light mesons is constructed and the mass spectrum is calculated. It is compared with experimental data.

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How to obtain a covariant Breit type equation from relativistic constraint theory

Abstract: It is shown that, by an appropriate modification of the structure of the interaction potential, the Breit equation can be incorporated into a set of two compatible manifestly covariant wave equations, derived from the general rules of Constraint Theory.

Cited by 22 publications

References 35 publications

Singularity-Free Breit Equation From Constraint Two-Body Dirac Equations

Singularity-Free Breit Equation From Constraint Two-Body Dirac Equations

Relativistic calculation of the meson spectrum: A fully covariant treatment versus standard treatments

Solvable Two-Body Dirac Equation as a Potential Model of Light Mesons

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