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Exact Solutions of Bethe-Salpeter Equations with Instantaneous Interactions
High Energy Physics - Phenomenology · Submitted 20 Nov 2012
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim Under suitable simplifying assumptions about the systems discussed, we derive analytically some examples of rigorous solutions to the instantaneous homogeneous Bethe-Salpeter equation by relating tentative solutions to the interactions responsible for the formation of bound states.
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The Bethe-Salpeter approach allows for quantum-field-theoretic descriptions of relativistic bound states; its inherent complexity, however, usually prevents to find its exact solutions. Under suitable simplifying assumptions about the systems discussed, we derive analytically some examples of rigorous solutions to the instantaneous homogeneous Bethe-Salpeter equation by relating tentative solutions to the interactions responsible for the formation of bound states.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | The Bethe-Salpeter approach allows for quantum-field-theoretic descriptions of relativistic bound states; its inherent complexity, however, usually prevents to find its exact solutions. | background 0.93 | 0.06 | 0.05 | asserted 0.98 |
| s1 | Under suitable simplifying assumptions about the systems discussed, we derive analytically some examples of rigorous solutions to the instantaneous homogeneous Bethe-Salpeter equation by relating tentative solutions to the interactions responsible for the formation of bound states. | contribution 0.93 | 0.96 | 0.81 | asserted 1.00 |
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The paper
Original abstract
The Bethe-Salpeter approach allows for quantum-field-theoretic descriptions of relativistic bound states; its inherent complexity, however, usually prevents to find its exact solutions. Under suitable simplifying assumptions about the systems discussed, we derive analytically some examples of rigorous solutions to the instantaneous homogeneous Bethe-Salpeter equation by relating tentative solutions to the interactions responsible for the formation of bound states.
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How the literature uses it
12 arXiv papers cite this in 23 sentences
Papers citing it · 16 sentences without a confident label
Uses its method or tool 7 papers
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The application of suitably adapted inversion techniques [ref] allows us to retrieve all the underlying interactions — rooted, of course, in QCD — analytically in the form of a (configuration-space) central potential $V(r),$ $r≡|x|,$ from presumed solutions to the Bethe–Salpeter equation [ref] .
Janus-Facedness of the Pion: Analytic Instantaneous Bethe-Salpeter Models · Introduction: quark–antiquark bound states of Goldstone-boson identity · 0.94
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The actual goal of our inversion technique [ref] is, for a given bound-state Salpeter amplitude $ϕ(),$ the extraction of the underlying configuration-space potential $V(r)$ from the relevant bound-state equation carved out within a sufficiently simplified Bethe–Salpeter formalism.
Light Pseudoscalar Mesons in Bethe-Salpeter Equation with Instantaneous Interaction · Inversion Procedure · 0.95
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In Euclidean-space representation, indicated by underlining the corresponding variables, this relation between Bethe–Salpeter amplitude and the quark propagator functions $M(k^2)$ and $Z(k^2)$ can be reformulated as [ref] [equation] This relation can be capitalized to convert, by inversion [ref] , knowledge about the behaviour of the fermion propagator into information about the underlying effective quark–antiquark interactions [ref] .
Goldstonic pseudoscalar mesons in Bethe-Salpeter-inspired setting · Inversion of Dyson–Schwinger Propagator Solution · 0.85
What it cites · 26 sentences without a confident label
Cites as background 16 papers
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In the following, we intend to exemplify our technique of constructing exact solutions to the reduced Salpeter equation by considering only a few of those Lorentz structures $Γ⊗Γ$ of the interaction kernel $K(p,q)$ that are commonly used in phenomenological descriptions of hadrons, notably, of mesons, as bound states of quarks confined by the strong interactions.[Since the first encounter [ref] of unstable solutions of Salpeter equations with confining interactions, the stability of solutions of different relativistic bound-state equations has been an issue of concern [ref] .
The stability of the spectator, Dirac, and Salpeter equations for mesons · Radial Eigenvalue Equations · 0.93
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In the following, we intend to exemplify our technique of constructing exact solutions to the reduced Salpeter equation by considering only a few of those Lorentz structures $Γ⊗Γ$ of the interaction kernel $K(p,q)$ that are commonly used in phenomenological descriptions of hadrons, notably, of mesons, as bound states of quarks confined by the strong interactions.[Since the first encounter [ref] of unstable solutions of Salpeter equations with confining interactions, the stability of solutions of different relativistic bound-state equations has been an issue of concern [ref] .
Bound q bar q systems in the framework of different versions of 3D reductions of the Bethe-Salpeter equation · Radial Eigenvalue Equations · 0.93
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In the following, we intend to exemplify our technique of constructing exact solutions to the reduced Salpeter equation by considering only a few of those Lorentz structures $Γ⊗Γ$ of the interaction kernel $K(p,q)$ that are commonly used in phenomenological descriptions of hadrons, notably, of mesons, as bound states of quarks confined by the strong interactions.[Since the first encounter [ref] of unstable solutions of Salpeter equations with confining interactions, the stability of solutions of different relativistic bound-state equations has been an issue of concern [ref] .
Bound q-bar q systems in the framework of two-body Dirac equations obtained from different versions of 3D-reductions of the Bethe-Salpeter Equations · Radial Eigenvalue Equations · 0.93
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