Relationship of Field-Theory Based Single-Boson-Exchange Potentials to Static Ones

Amghar, A.; Desplanques, B.

doi:10.1007/s006010070025

Cited by 6 publications

(22 citation statements)

References 38 publications

(141 reference statements)

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“…Notice that, up to order 1 m 0 , this cancellation is expected to hold at all orders in the coupling g 2 , i.e. even including multi-boson exchange diagrams [9]. The effective interaction is thus also given by V 0 in this case.…”

Section: General Casementioning

confidence: 87%

“…As we do not pay much attention to contributions of order g 6 , one could be tempted to drop terms like E −e−e ′ in the denominator of Eq. (9), which are of the same order. Doing this also has the advantage that the integral of Eq.…”

mentioning

confidence: 90%

“…The transformation which was performed here is more in the spirit of the Foldy-Wouthuysen one (see ref. [9] for details). It implicitly corresponds to introducing effective degrees of freedom with the drawback that the interaction generally acquires a non-local character.…”

Section: Energy-independent Approach and Effective Interactionmentioning

confidence: 99%

“…In the present work, we will improve upon this approximation, extending to massive bosons what was done in ref. [9] for the zero-mass case. In the latter one, the Coulomb-like potential kept its analytical form, only the coupling constant was renormalized by a factor that was determined by solving a self-consistency equation.…”

Section: Energy-independent Approach and Effective Interactionmentioning

confidence: 99%

“…(9,38,39) but without the isospin operators O i . The factor κ is the result of the isospin algebra.…”

Section: General Casementioning

confidence: 99%

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From the Bethe–Salpeter equation to nonrelativistic approaches with effective two-body interactions

Amghar

Desplanques²,

Theußl³

2001

Nuclear Physics A

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It is known that binding energies calculated from the Bethe-Salpeter equation in ladder approximation can be reasonably well accounted for by an energy-dependent interaction, at least for the lowest states. It is also known that none of these approaches gives results close to what is obtained by using the same interaction in the so-called instantaneous approximation, which is often employed in non-relativistic calculations. However, a recently proposed effective interaction was shown to account for the main features of both the Bethe-Salpeter equation and the energydependent approach. In the present work, a detailed comparison of these different methods for calculating binding energies of a two-particle system is made. Some improvement, previously incorporated for the zero-mass boson case in the derivation of the effective interaction, is also employed for massive bosons. The constituent particles are taken to be distinguishable and spinless. Different masses of the exchanged boson (including a zero mass) as well as states with different angular momenta are considered and the contribution of the crossed two-boson exchange diagram is discussed. With this respect, the role played by the charge of the exchanged boson is emphasized. It is shown that the main difference between the Bethe-Salpeter results and the instantaneous approximation ones are not due to relativity as often conjectured.

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Section: General Casementioning

confidence: 87%

mentioning

confidence: 90%

Section: Energy-independent Approach and Effective Interactionmentioning

confidence: 99%

Section: Energy-independent Approach and Effective Interactionmentioning

confidence: 99%

“…(9,38,39) but without the isospin operators O i . The factor κ is the result of the isospin algebra.…”

Section: General Casementioning

confidence: 99%

See 3 more Smart Citations

From the Bethe–Salpeter equation to nonrelativistic approaches with effective two-body interactions

Amghar

Desplanques²,

Theußl³

2001

Nuclear Physics A

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A variational calculation of particle-antiparticle bound states in the scalar Yukawa model

Ding

Darewych

2000

J. Phys. G: Nucl. Part. Phys.

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We consider particle-antiparticle bound states in the scalar Yukawa (Wick-Cutkosky) model. The variational method in the Hamiltonian formalism of quantum field theory is employed. A reformulation of the model is studied, in which covariant Green functions are used to solve for the mediating field in terms of the particle fields. A simple Fock-state variational ansatz is used to derive a relativistic equation for the particle-antiparticle states. This equation contains one-quantum-exchange and virtual-annihilation interactions. It is shown that analytic solutions of this equation can be obtained for the simplified case where only the virtual-annihilation interaction is retained. More generally, numerical and perturbative solutions of the equation are obtained for the massive and massless exchange cases. We compare our results with various Bethe-Salpeter-based calculations.

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Form factors in the “point form” of relativistic quantum mechanics: Single- and two-particle currents

Desplanques¹,

Theußl²

2004

Eur. Phys. J. A

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Electromagnetic and Lorentz-scalar form factors are calculated for a bound system of two spinless particles exchanging a zero-mass scalar particle. Different approaches are considered including solutions of a Bethe-Salpeter equation, a "point form" approach to relativistic quantum mechanics and a non-relativistic one. The comparison of the Bethe-Salpeter results, which play the role of an "experiment" here, with the ones obtained in "point form" in single-particle approximation, evidences sizable discrepancies, pointing to large contributions from two-body currents in the latter approach. These ones are constructed using two constraints: ensuring current conservation and reproducing the Born amplitude. The two-body currents so obtained are qualitatively very different from standard ones. Quantitatively, they turn out not to be sufficient to remedy all the shortcomings of the "point form" form factors evidenced in impulse approximation.

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Relationship of Field-Theory Based Single-Boson-Exchange Potentials to Static Ones

Cited by 6 publications

References 38 publications

From the Bethe–Salpeter equation to nonrelativistic approaches with effective two-body interactions

From the Bethe–Salpeter equation to nonrelativistic approaches with effective two-body interactions

A variational calculation of particle-antiparticle bound states in the scalar Yukawa model

Form factors in the “point form” of relativistic quantum mechanics: Single- and two-particle currents

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