Cross-ladder effects in Bethe-Salpeter and light-front equations

Carbonell, J.; Karmanov, V. A.

doi:10.1140/epja/i2005-10194-y

Cited by 77 publications

(141 citation statements)

References 14 publications

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“…[5,6] the BS amplitude is represented as an integral over a weight function g -the so called Nakanishi transform [7] -which satisfies a nonsingular equation. A modification of this method, based on the light-front projection of the BS amplitude, was developed in [8][9][10][11][12] and used to find the bound state Minkowski BS amplitude. The elastic EM form factor was also calculated in [13].…”

Section: Introductionmentioning

confidence: 99%

Transition electromagnetic form factor and current conservation in the Bethe-Salpeter approach

Carbonell

Karmanov

2015

Phys. Rev. D

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The transition form factor for electrodisintegration of a two-body bound system is calculated in the Bethe-Salpeter framework. For the initial (bound) and the final (scattering) states, we use our solutions of the Bethe-Salpeter equation in Minkowski space which were first obtained recently. The gauge invariance, which manifests itself in the conservation of the transition electromagnetic current J · q = 0, is studied numerically. It results from a cancellation between the plane wave and the final state interaction contributions. This cancellation takes place only if the initial bound state BS amplitude, the final scattering state and the operator of electromagnetic current are strictly consistent with each other, that is if they are found in the same dynamical framework. A reliable result for the transition form factor can be obtained in this case only.

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Section: Introductionmentioning

confidence: 99%

Transition electromagnetic form factor and current conservation in the Bethe-Salpeter approach

Carbonell

Karmanov

2015

Phys. Rev. D

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“…Notably, the numerator of each c ij (k, k , p) can contain the third power of the four-momentum k, at the most. In complete analogy with the two-scalar interacting system, where only one amplitude is present [3][4][5][6][7][8][9], one can introduce NIR for each amplitudes φ i , viz…”

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confidence: 99%

Advances in solving the two-fermion homogeneous Bethe-Salpeter equation in Minkowski space

et al. 2016

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Actual solutions of the Bethe-Salpeter equation for a two-fermion bound system are becoming available directly in Minkowski space, by virtue of a novel technique, based on the so-called Nakanishi integral representation of the Bethe-Salpeter amplitude and improved by expressing the relevant momenta through light-front components, i.e. k ± = k 0 ± k 3 . We solve a crucial problem that widens the applicability of the method to real situations by providing an analytically exact treatment of the singularities plaguing the two-fermion problem in Minkowski space, irrespective of the complexity of the irreducible Bethe-Salpeter kernel. This paves the way for feasible numerical investigations of relativistic composite systems, with any spin degrees of freedom. We present a thorough comparison with existing numerical results, evaluated in both Minkowski and Euclidean space, fully corroborating our analytical treatment, as well as fresh light-front amplitudes illustrating the potentiality of non perturbative calculations performed directly in Minkowski space.

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“…A similar approach combined with the light-front projection was proposed in [4,5]. It led to a different integral equation which involved only smooth functions and was numerically easy to treat.…”

Section: Introductionmentioning

confidence: 99%

“…The bound state Minkowski amplitude and later on [6,8] the corresponding form factors were in this way computed for the first time. A modified method to the one developed in [4,5] aimed to compute the scattering states was proposed in [9]. It has already been successfully tested for the bound states [15].…”

Section: Introductionmentioning

confidence: 99%