A Relativistic Equation for Bound-State Problems

Salpeter, E. E.; Bethe, Hans A.

doi:10.1103/physrev.84.1232

Cited by 2,539 publications

(1,978 citation statements)

References 8 publications

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“…In practice it is then much simpler to derive self-consistent relations for these objects since they contain the full information about the hadron on its pole. The resulting integral equations are known as homogeneous Bethe-Salpeter equations [286][287][288], or alternatively Faddeev equations in the case of baryons [289,290], or simply hadronic bound-state equations. In the following we discuss their properties and demonstrate how Bethe-Salpeter equations are obtained in the functional framework.…”

Section: Bound-state Equationsmentioning

confidence: 99%

Baryons as relativistic three-quark bound states

Eichmann

Sanchis-Alepuz

Williams

et al. 2016

Progress in Particle and Nuclear Physics

418

530

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We review the spectrum and electromagnetic properties of baryons described as relativistic three-quark bound states within QCD. The composite nature of baryons results in a rich excitation spectrum, whilst leading to highly non-trivial structural properties explored by the coupling to external (electromagnetic and other) currents. Both present many unsolved problems despite decades of experimental and theoretical research. We discuss the progress in these fields from a theoretical perspective, focusing on nonperturbative QCD as encoded in the functional approach via Dyson-Schwinger and Bethe-Salpeter equations. We give a systematic overview as to how results are obtained in this framework and explain technical connections to lattice QCD. We also discuss the mutual relations to the quark model, which still serves as a reference to distinguish 'expected' from 'unexpected' physics. We confront recent results on the spectrum of non-strange and strange baryons, their form factors and the issues of two-photon processes and Compton scattering determined in the DysonSchwinger framework with those of lattice QCD and the available experimental data. The general aim is to identify the underlying physical mechanisms behind the plethora of observable phenomena in terms of the underlying quark and gluon degrees of freedom.

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Section: Bound-state Equationsmentioning

confidence: 99%

Baryons as relativistic three-quark bound states

Eichmann

Sanchis-Alepuz

Williams

et al. 2016

Progress in Particle and Nuclear Physics

418

530

View full text Add to dashboard Cite

show abstract

“…In the standard scheme, the quasiparticle band structures are obtained using the Green's function G and screened Coulomb interaction W approximation, 7 while optical excitation energies are obtained by solving a Bethe-Salpeter equation (BSE) 8 with a statically screened electron-hole interaction. The GW-BSE approach 9,10 has been successfully applied to a number of different systems ranging from bulk semiconductors, 9 insulators and their surfaces, 11 two-dimensional systems such as graphene 12 and boron nitride layers, 13 metal-molecule interfaces, 6 isolated molecules, [14][15][16] and liquid water.…”

Section: Introductionmentioning

confidence: 99%

Optical properties of bulk semiconductors and graphene/boron nitride: The Bethe-Salpeter equation with derivative discontinuity-corrected density functional energies

2012

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We present an efficient implementation of the Bethe-Salpeter equation (BSE) for optical properties of materials in the projector augmented wave method GPAW. Single-particle energies and wave functions are obtained from the GLLBSC functional which explicitly includes the derivative discontinuity, is computationally inexpensive, and yields excellent fundamental gaps. Electron-hole interactions are included through the BSE using the statically screened interaction evaluated in the random phase approximation. For a representative set of semiconductors and insulators we find excellent agreement with experiments for the dielectric functions, onset of absorption, and lowest excitonic features. For the two-dimensional systems of graphene and hexagonal boron-nitride (h-BN) we find good agreement with previous many-body calculations. For the graphene/h-BN interface, we find that the fundamental and optical gaps of the h-BN layer are reduced by 2.0 eV and 0.7 eV, respectively, compared to freestanding h-BN. This reduction is due to image charge screening which shows up in the GLLBSC calculation as a reduction (vanishing) of the derivative discontinuity.

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“…Understanding the discrepancies for binding energies obtained from different approaches, ranging from the ladder Bethe-Salpeter equation at one extreme [1] to a non-relativistic equation with a so-called instantaneous one-boson exchange interaction at the other extreme, has been and is still a subject which raises considerable interest and curiosity [2][3][4][5][6][7][8][9][10]. Although it is more founded theoretically, the Bethe-Salpeter equation in its simplest form (along with other approaches) is not doing as well as the Dirac or Klein-Gordon equation in reproducing the spectrum of atomic systems.…”

Section: Introductionmentioning

confidence: 99%

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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A Relativistic Equation for Bound-State Problems

Cited by 2,539 publications

References 8 publications

Baryons as relativistic three-quark bound states

Baryons as relativistic three-quark bound states

Optical properties of bulk semiconductors and graphene/boron nitride: The Bethe-Salpeter equation with derivative discontinuity-corrected density functional energies

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

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