scholarly journals Critical Stability of Three-Body Relativistic Bound States with Zero-Range Interaction

2004 ◽  
Vol 34 (1-3) ◽  
Author(s):  
V. A. Karmanov ◽  
J. Carbonell
Keyword(s):  
Bound States ◽  
Critical Stability ◽  
Range Interaction ◽  
Zero Range ◽  
Three Body ◽  
Relativistic Bound States

scholarly journals Three-body bound states with zero-range interaction in the Bethe–Salpeter approach

2017 ◽  
Vol 770 ◽  
pp. 131-137 ◽  
Author(s):  
E. Ydrefors ◽  
J.H. Alvarenga Nogueira ◽  
V. Gigante ◽  
T. Frederico ◽  
V.A. Karmanov
Keyword(s):  
Bound States ◽  
Range Interaction ◽  
Zero Range ◽  
Three Body

scholarly journals Bethe-Salpeter approach to three-body bound states with zero-range interaction

2019 ◽  
Vol 1291 ◽  
pp. 012013
Author(s):  
E Ydrefors ◽  
J H Alvarenga Nogueira ◽  
V A Karmanov ◽  
T Frederico
Keyword(s):  
Bound States ◽  
Range Interaction ◽  
Zero Range ◽  
Three Body

scholarly journals Studies of three-body bound states with zero-range interaction in Minkowski space

2020 ◽  
Author(s):  
Emanuel Ydrefors ◽  
Jorge H Alvarenga Nogueira ◽  
Vladimir Karmanov ◽  
Tobias Frederico
Keyword(s):  
Minkowski Space ◽  
Bound States ◽  
Range Interaction ◽  
Zero Range ◽  
Three Body

Three-Body System with Two-Channel Zero-Range Interaction Model of Feshbach Resonance

2010 ◽  
Vol 50 (1-4) ◽  
pp. 417-421 ◽  
Author(s):  
P. K. Sørensen ◽  
D. V. Fedorov ◽  
A. S. Jensen
Keyword(s):  
Feshbach Resonance ◽  
Interaction Model ◽  
Body System ◽  
Range Interaction ◽  
Zero Range ◽  
Three Body

Quantum Numbers of Eigenstates of Generalized de Broglie-Bargmann- Wigner Equations for Fermions with Partonic Substructure

2003 ◽  
Vol 58 (1) ◽  
pp. 1-12 ◽  
Author(s):  
H. Stumpf
Keyword(s):  
Angular Momentum ◽  
Integral Equations ◽  
Bound States ◽  
Solution Space ◽  
Many Body ◽  
Quantum Numbers ◽  
Relevant Group ◽  
Three Body ◽  
Relativistic Bound States ◽  
Fusion Theory

Generalized de Broglie-Bargmann-Wigner (BBW) equations are relativistically invariant quantum mechanical many body equations with nontrivial interaction, selfregularization and probability interpretation. Owing to these properties these equations are a suitable means for describing relativistic bound states of fermions. In accordance with de Broglie’s fusion theory and modern assumptions about the partonic substructure of elementary fermions, i.e., leptons and quarks, the three-body generalized BBW-equations are investigated. The transformation properties and quantum numbers of the three-parton equations under the relevant group actions are elaborated in detail. Section 3 deals with the action of the isospin group SU(2), a U(1) global gauge group for the fermion number, the hypercharge and charge generators. The resulting quantum numbers of the composite partonic systems can be adapted to those of the phenomenological particles to be described. The space-time transformations and in particular rotations generated by angular momentum operators are considered in Section 4. Based on the compatibility of the BBW-equations and the group theoretical constraints, in Sect. 5 integral equations are formulated in a representation with diagonal energy and total angular momentum variables. The paper provides new insight into the solution space and quantum labels of resulting integral equations for three parton states and prepares the ground for representing leptons and quarks as composite systems.

scholarly journals Models of zero-range interaction for the bosonic trimer at unitarity

2020 ◽  
pp. 2150010
Author(s):  
Alessandro Michelangeli
Keyword(s):  
Quadratic Forms ◽  
Bound States ◽  
Scattering Length ◽  
The Self ◽  
Correct Identification ◽  
Range Interaction ◽  
Canonical Models ◽  
Von Neumann ◽  
Short Scale ◽  
Zero Range

We present the mathematical construction of the physically relevant quantum Hamiltonians for a three-body system consisting of identical bosons mutually coupled by a two-body interaction of zero range. For a large part of the presentation, infinite scattering length will be considered (the unitarity regime). The subject has several precursors in the mathematical literature. We proceed through an operator-theoretic construction of the self-adjoint extensions of the minimal operator obtained by restricting the free Hamiltonian to wave-functions that vanish in the vicinity of the coincidence hyperplanes: all extensions thus model an interaction precisely supported at the spatial configurations where particles come on top of each other. Among them, we select the physically relevant ones, by implementing in the operator construction the presence of the specific short-scale structure suggested by formal physical arguments that are ubiquitous in the physical literature on zero-range methods. This is done by applying at different stages the self-adjoint extension schemes à la Kreĭn–Višik–Birman and à la von Neumann. We produce a class of canonical models for which we also analyze the structure of the negative bound states. Bosonicity and zero range combined together make such canonical models display the typical Thomas and Efimov spectra, i.e. sequence of energy eigenvalues accumulating to both minus infinity and zero. We also discuss a type of regularization that prevents such spectral instability while retaining an effective short-scale pattern. Beside the operator qualification, we also present the associated energy quadratic forms. We structured our analysis so as to clarify certain steps of the operator-theoretic construction that are notoriously subtle for the correct identification of a domain of self-adjointness.

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