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

Ding, Bingfeng; Darewych, Jurij W.

doi:10.1088/0954-3899/26/6/312

Cited by 35 publications

(62 citation statements)

References 60 publications

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“…If we now useΛ = Λ − Λ ′ , instead of Λ, in and (11)(12)(13), we obtain the spectrum, (11)(12)(13)(14)(15)(16) which coincides with the results of Connell [35] and Hersbach [37] for the parity (−1) J±1 states. Thus, correcting for the spurious terms in the Breit Hamiltonian, we obtain the expected O(α 4 ) results.…”

Section: Perturbative Solutions For J > 0 Statessupporting

confidence: 81%

“…8 Perturbative determination of the relativistic correction to the two-body eigenenergies for J = 0 states Equations (7)(8)(9)(10)(11)(12)(13)(14)(15)(16)(17)(18)(19)(20) can be written in the matrix form H|ψ = ǫ|ψ where If we expand the coefficients W f and W g (Eqs. (7-10) and (7-11)) in powers of V /m i , and keep only the lowest-order terms, we obtain …”

Section: Two-body Equation In the Lorentz Gaugementioning

confidence: 99%

“…Then the matrixH takes the form (10)(11)(12)(13)(14)(15)(16)(17)(18) and the set of Eqs. (10-16) becomes…”

Section: Radial Reduction For J > 0 Statesmentioning

confidence: 99%

“…4 . But any two solutions of (10)(11)(12)(13)(14)(15)(16)(17)(18)(19)(20)(21)(22), X 1 and Y 1 , corresponding to different values of the energy, E and E ′ , are not orthogonal. This is due to the nonlinear dependence of L(E) on E. Orthogonality can be instated by using the following definition of inner product: …”

Section: Radial Reduction For J > 0 Statesmentioning

confidence: 99%

“…In the P = (−1) J case, the matrix J is not diagonal: , (11)(12)(13)(14)(15)(16)(17)(18)(19) so that the 0th-order Hamiltonian becomes: -20) It possesses the doubly degenerate eigenvalues (11-9) with eigenstates: The first-order correctionH (1) , with the matrices K(ρ, λ) = 1 8 The energy spectrum (11-13) with λ…”

Section: Perturbative Solutions For J > 0 Statesmentioning

confidence: 99%

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Exact few-particle eigenstates in partially reduced QED

Darewych

Duviryak

2002

Phys. Rev. A

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We consider a reformulation of QED in which covariant Green functions are used to solve for the electromagnetic field in terms of the fermion fields. It is shown that exact few-fermion eigenstates of the resulting Hamiltonian can be obtained in the canonical equal-time formalism for the case where there are no free photons. These eigenstates lead to two-and three-body Dirac-like equations with electromagnetic interactions. Perturbative and some numerical solutions of the two-body equations are presented for positronium and muonium-like systems, for various strengths of the coupling.

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Section: Perturbative Solutions For J > 0 Statessupporting

confidence: 81%

Section: Two-body Equation In the Lorentz Gaugementioning

confidence: 99%

“…Then the matrixH takes the form (10)(11)(12)(13)(14)(15)(16)(17)(18) and the set of Eqs. (10-16) becomes…”

Section: Radial Reduction For J > 0 Statesmentioning

confidence: 99%

Section: Radial Reduction For J > 0 Statesmentioning

confidence: 99%

Section: Perturbative Solutions For J > 0 Statesmentioning

confidence: 99%

See 3 more Smart Citations

Exact few-particle eigenstates in partially reduced QED

Darewych

Duviryak

2002

Phys. Rev. A

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Comparison of Relativistic Bound-State Calculations in Front-Form and Instant-Form Dynamics

2003

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Using the Wick-Cutkosky model and an extended version (massive exchange) of it, we have calculated the bound states in a quantum field theoretical approach. In the light-front formalism we have calculated the bound-state mass spectrum and wave functions. Using the Terent'ev transformation we can write down an approximation for the angular dependence of the wave function. After calculating the bound-state spectra we characterized all states found. Similarly, we have calculated the bound-state spectrum and wave functions in the instant-form formalism. We compare the spectra found in both forms of dynamics in the ladder approximation and show that in both forms of dynamics the O(4) symmetry is broken.

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Variational Worldline Approximation for the Relativistic Two-Body Bound State in a Scalar Model

2006

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We use the worldline representation of field theory together with a variational approximation to determine the lowest bound state in the scalar Wick-Cutkosky model where two equal-mass constituents interact via the exchange of mesons. Self-energy and vertex corrections are included approximately in a consistent way as well as crossed diagrams. Only vacuumpolarization effects of the heavy particles are neglected. In a path integral description of an appropriate current-current correlator an effective, retarded action is obtained by integrating out the meson field. As in the polaron problem we employ a quadratic trial action with variational functions to describe retardation and binding effects through multiple meson exchange. The variational equations for these functions are derived, discussed qualitatively and solved numerically. We compare our results with the ones from traditional approaches based on the Bethe-Salpeter equation and find an enhanced binding contrary to some claims in the literature. For weak coupling this is worked out analytically and compared with results from effective field theories. However, the well-known instability of the model, which usually is ignored, now appears at smaller coupling constants than in the one-body case and even when self-energy and vertex corrections are turned off. This induced instability is investigated analytically and the width of the bound state above the critical coupling is estimated.1 Frequently only the exact solution of the ladder BSe for massless exchange particles is called the "Wick-Cutkosky model". Here we use this designation in a more general sense for a class of scalar models described by Lagrangians of the form (1.1,1.2).

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

Cited by 35 publications

References 60 publications

Exact few-particle eigenstates in partially reduced QED

Exact few-particle eigenstates in partially reduced QED

Comparison of Relativistic Bound-State Calculations in Front-Form and Instant-Form Dynamics

Variational Worldline Approximation for the Relativistic Two-Body Bound State in a Scalar Model

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