Solutions of the three-magnon bound state equation. III. The physical eigenstate

Chanchal K. Majumdar; Indrani Bose

doi:10.1063/1.523551

Derivation of the three-body bound-state equation from the effective action

Physical Review D ◽

10.1103/physrevd.40.2654 ◽

1989 ◽

Vol 40 (8) ◽

pp. 2654-2661 ◽

Cited By ~ 5

Author(s):

M. Komachiya ◽

M. Ukita ◽

R. Fukuda

Keyword(s):

Effective Action ◽

Bound State ◽

State Equation ◽

Three Body

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Convariant single-time bound-state equation

Physics Letters B ◽

10.1016/0370-2693(95)00568-6 ◽

1995 ◽

Vol 353 (2-3) ◽

pp. 284-288 ◽

Cited By ~ 4

Author(s):

O.W. Greenberg ◽

R. Ray ◽

F. Schlumpf

Keyword(s):

Bound State ◽

State Equation ◽

Single Time

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The spinless relativistic kink-like problem

International Journal of Modern Physics A ◽

10.1142/s0217751x15500621 ◽

2015 ◽

Vol 30 (12) ◽

pp. 1550062 ◽

Cited By ~ 3

Author(s):

Wolfgang Lucha ◽

Franz F. Schöberl

Keyword(s):

Quantum Theory ◽

Eigenvalue Problem ◽

Schrödinger Equation ◽

Boundary Conditions ◽

Schrodinger Equation ◽

Bound State ◽

State Equation ◽

Hyperbolic Tangent ◽

Central Potential ◽

All Solutions

We constrain the possible bound-state solutions of the spinless Salpeter equation (the most obvious semirelativistic generalization of the nonrelativistic Schrödinger equation) with an interaction between the bound-state constituents given by the kink-like potential (a central potential of hyperbolic-tangent form) by formulating a bunch of very elementary boundary conditions to be satisfied by all solutions of the eigenvalue problem posed by a bound-state equation of this type, only to learn that all results produced by a procedure very much liked by some quantum-theory practitioners prove to be in severe conflict with our expectations.

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ENERGY SPECTRA OF GLUINONIUM

International Journal of Modern Physics E ◽

10.1142/s0218301311040803 ◽

2011 ◽

Vol 20 (supp02) ◽

pp. 200-209

Author(s):

CÉSAR A. Z. VASCONCELLOS ◽

DIMITER HADJIMICHEF ◽

MÁRIO L. L. DA SILVA ◽

MOISÉS RAZEIRA ◽

ALEXANDRE MESQUITA ◽

...

Keyword(s):

Energy Spectrum ◽

Excited States ◽

Bound States ◽

Bound State ◽

State Equation ◽

Relativistic Case ◽

Light Scalar ◽

Pseudo Scalar ◽

Relativistic Bound States

We investigate relativistic bound states for a hypothetical light scalar gluino pair (gluinonium), in the framework of the covariant Bethe-Salpeter equation (BSE). In this paper, we derive, from the covariant BSE for a fermion-anti-fermion system, using charge conjugation, the corresponding bound-state equation for a gluino pair and we then formulate, for a static harmonic kernel, the coupled differential equations for the corresponding static Bethe-Salpeter amplitude. The steps of our approach then include a numerical solution of the Bethe-Salpeter amplitude for a two-body interaction consisting of scalar, pseudo-scalar, and four-vector components and the determination of the energy spectrum for the ground and the radially excited states of massive gluinonium. We found the energy spectrum and radial distributions of fundamental and excited states of gluinonium. The comparison of the values obtained in the extreme relativistic case with the corresponding values predicted by a harmonic oscillator potential model shows that there is good agreement between the two formulations. The predictions of the binding energy of glunionium in the non-relativistic model are however systematically higher.

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THE GROSS–NEVEU MODEL ON THE LIGHT-CONE

Modern Physics Letters A ◽

10.1142/s0217732395000569 ◽

1995 ◽

Vol 10 (06) ◽

pp. 525-537 ◽

Cited By ~ 5

Author(s):

IGOR PESANDO

Keyword(s):

Light Cone ◽

Bound State ◽

State Equation ◽

Coupling Constant ◽

Normal Ordering ◽

Running Coupling ◽

Running Coupling Constant ◽

Light Cone Quantization ◽

Gross Neveu Model

We consider the (massive) Gross–Neveu model using the light-cone quantization where we solve the constraints explicitly. We show that the vacuum is trivial and that the quantization fails when m = 0. We show that the running coupling constant emerges as a pure normal ordering effect and we discuss the bound state equation.

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THE BOUND STATE EQUATION FOR TWO GLUONS AND ITS SOLUTION

International Journal of Modern Physics A ◽

10.1142/s0217751x9900107x ◽

1999 ◽

Vol 14 (13) ◽

pp. 2117-2132

Author(s):

J. Y. CUI ◽

J. M. WU

Keyword(s):

Field Theory ◽

Relativistic Quantum ◽

Bound State ◽

State Equation ◽

Exchange Potential ◽

Quantum Field ◽

Relativistic Quantum Field Theory ◽

Lattice Calculation ◽

Confining Potential ◽

Instantaneous Approximation

We derive the bound state equation for two gluons in relativistic quantum field theory, i.e. the Bethe–Salpeter (BS) equation for two gluons. To solve it, we choose the kernel as the sum of a one-gluon exchange potential, a contact interaction and a linear confining potential. Under instantaneous approximation, this BS equation is solved numerically. The spectrum and the BS wave function of the glueballs are obtained in this framework. The numerical results are in agreement with that of recent lattice calculation.

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