A variational calculation of particle--antiparticle bound states in the scalar Yukawa model

Ding, Bingfeng; Darewych, Jurij W.

doi:10.1088/0954-3899/27/2/701

Cited by 11 publications

(15 citation statements)

References 37 publications

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“…For the sake of completeness and having a self-contained paper it is better to recall some of the main points from previous works [12,13]. The Lagrangian density for scalar particles which interact via a mediating scalar field is where g indicates the coupling constant.…”

Section: Variational Methods and The Reformulated Modelmentioning

confidence: 99%

“…As it has been mentioned, for example, in [7] or [12,13] the theories based on (2.1) and (2.2) are equivalent in the sense that they lead to the same invariant matrix elements in different orders of perturbation theory. The Lagrangian density (2.2) can be written as: …”

Section: Variational Methods and The Reformulated Modelmentioning

confidence: 99%

“…As mentioned before, the case of two-body system has been investigated before [12,13]. However, it is good to recall some key points of the two-body particle and antiparticle system since it will help to better understand the four-and six-body cases.…”

Section: ð3:7þmentioning

confidence: 99%

“…Figure 1 of Ref. [12,13] (which is plotted here again as Fig. 1) contains various results of WC or BS formalism as well as other calculations.…”

Section: ð3:7þmentioning

confidence: 99%

“…The case of two-body system has been investigated before [12,13]. However, we remind it again here to better follow the four-and six-body cases.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Study of virtual annihilation and retardation effects in relativistic two-, four-, and six-body wave equations in scalar QFT

Emami-Razavi

Asgary

2017

J Theor Appl Phys

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The variational method within the Hamiltonian formalism of QFT using Darewych reformulated model has been used for scalar particles and antiparticles interacting through a scalar mediating field. We have investigated the relativistic effects such as virtual annihilation interactions and retardation effects for relativistic two-, four-, and six-body wave equations in scalar QFT. Approximate ground-state solutions have been studied for different strengths of coupling, for both massive and massless mediating fields where the virtual annihilation terms or retardation effects in the wave equations have been included or eliminated.

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Section: Variational Methods and The Reformulated Modelmentioning

confidence: 99%

Section: Variational Methods and The Reformulated Modelmentioning

confidence: 99%

Section: ð3:7þmentioning

confidence: 99%

“…Figure 1 of Ref. [12,13] (which is plotted here again as Fig. 1) contains various results of WC or BS formalism as well as other calculations.…”

Section: ð3:7þmentioning

confidence: 99%

“…The case of two-body system has been investigated before [12,13]. However, we remind it again here to better follow the four-and six-body cases.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Study of virtual annihilation and retardation effects in relativistic two-, four-, and six-body wave equations in scalar QFT

Emami-Razavi

Asgary

2017

J Theor Appl Phys

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Relativistic n-body wave equations in scalar quantum field theory

Emami-Razavi¹

2006

Physics Letters B

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Relativistic two-, three- and four-body wave equations in scalar QFT

Emami-Razavi¹,

Darewych²

2005

J. Phys. G: Nucl. Part. Phys.

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We use the variational method within the Hamiltonian formalism of QFT to derive relativistic two-, three- and four-body wave equations for scalar particles interacting via a massive or massless mediating scalar field (the scalar Yukawa model). The Lagrangian of the theory is reformulated by using Green's functions to express the mediating field in terms of the particle fields. The QFT is then constructed from the resulting reformulated Hamiltonian. Simple Fock-space variational trial states are used to derive relativistic two-, three- and four-body equations. The equations are shown to have the Schrödinger non-relativistic limit, with Coulombic interparticle potentials in the case of a massless mediating field and Yukawa interparticle potentials in the case of a massive mediating field. Ground-state solutions of the relativistic equations are obtained approximately for various strengths of coupling, for both massive and massless mediating fields, and a comparison of the two-, three- and four-particle binding energies is presented.

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A variational calculation of particle--antiparticle bound states in the scalar Yukawa model

Cited by 11 publications

References 37 publications

Study of virtual annihilation and retardation effects in relativistic two-, four-, and six-body wave equations in scalar QFT

Study of virtual annihilation and retardation effects in relativistic two-, four-, and six-body wave equations in scalar QFT

Relativistic n-body wave equations in scalar quantum field theory

Relativistic two-, three- and four-body wave equations in scalar QFT

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