Relativistic wave equations of<i>n</i>-body systems of particles and antiparticles of various masses in scalar quantum field theory

Emami-Razavi, Mohsen; Bergeron, Nantel; Darewych, Jurij W.

doi:10.1088/0954-3899/38/6/065004

Cited by 12 publications

(7 citation statements)

References 51 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…of the non-relativistic limit of eq. ( 31), is as expected, the n-body Schrödinger equation, (35) where…”

Section: Qed N-body Wave Equationssupporting

confidence: 74%

“…No (approximate) solutions of the relativistic four-fermion equation (47) have been obtained to date. The non-relativistic limit of (47) is, of course, equation (35) with n = 4.…”

Section: Two Three and Four-body Examplesmentioning

confidence: 99%

“…The variationally obtained n-body relativistic equations (31) (or non-relativistic equations (35) for n > 2) are not analytically solvable, hence approximate, usually variational, solutions must be obtained. Thus, for any n and any state, one can obtain an approximate variational solution for the energy E n and the wave-function of the n-body system by replacing F s 1 s 2 ...sn (p 1 , ..., p n ) with analytic functions containing adjustable features (parameters) to compute the energy expectation value (see Eqs.…”

Section: Qed N-body Wave Equationsmentioning

confidence: 99%

See 2 more Smart Citations

RELATIVISTIC WAVE EQUATIONS OF n-BODY SYSTEMS OF FERMIONS AND ANTIFERMIONS OF VARIOUS MASSES IN QUANTUM ELECTRODYNAMICS

Emami-Razavi

Bergeron

Darewych

2012

Int. J. Mod. Phys. E

Self Cite

View full text Add to dashboard Cite

The variational method in a reformulated Hamiltonian formalism of quantum electrodynamics (QED) is used to derive relativistic wave equations for systems consisting of n fermions and antifermions of various masses. The derived interaction kernels of these equations include one-photon exchange interactions. The equations have the expected Schrödinger non-relativistic limit. Application to some exotic few lepton systems is discussed briefly.Many-body fermion systems with electromagnetic interactions are the substance of atomic physics. Fundamental fermion and antifermion systems with electromagnetic interactions are of particular interest because they are "pure" QED systems, with point-like constituents and no nuclear force or size effects. Examples of such systems include positronium (Ps: e + e − ), muonium (Mu: µ + e − ) and their ions (Ps − : e + e − e − , Mu − : µ + e − e − ) and four-body systems such as Ps 2 (e + e − e + e − ) and Mu 2 (µ + e − µ + e − ). More generally, for "exotic atoms" such as e + PsH, Ps 2 O, Li + Ps 2 and Na + Ps 2 , nuclear size effects are not negligible. These have received attention in the past (e.g., Ref. 2).The problem of describing relativistic bound states in quantum field theory (QFT) was solved many years ago by Bethe and Salpeter (BS), 3,4 at least in principle. However, the BS method is not free of complications, such as the existence of relative-time coordinates, difficulty of implementation for systems of more than two bodies, and in practice, the perturbative treatment of interactions. There are many papers available in the literature that use the BS method, at least for twoand three-body systems. For example, Adkins and co-workers 5,6 have used BS formalism for the calculation of recoil corrections to the energy levels of hydrogenic ions, and a discussion of issues that will have to be treated for the many-electron case, where highly accurate experiments have been carried out, is given. Using a different approach than the BS formalism, Barut 7 summarized his previous work (including work with his co-authors) and generalized his two-body QED equation to many-body particles interacting via the exchange of massless vector bosons. In his formulation, 7 the relativistic many-body problem has a structure that is similar to that of the Schrödinger many-body problem.An alternative to the BS and other approaches is the variational method within the reformulated Hamiltonian formalism of QFT, introduced by Darewych. 8-10 Among the appealing features of this approach is that it is straightforwardly generalizable to systems of more than two particles, and it can be cast in the form of a relativistic generalization of the Schrödinger description of n-body systems. As a variational method it is applicable, at least in principle, to strongly coupled systems for which perturbation theory may be unreliable. It has disadvantages as well, particularly in that it may not be manifestly covariant, and like all variational methods, the construction of realistic yet tractable trial states may be...

show abstract

“…of the non-relativistic limit of eq. ( 31), is as expected, the n-body Schrödinger equation, (35) where…”

Section: Qed N-body Wave Equationssupporting

confidence: 74%

“…No (approximate) solutions of the relativistic four-fermion equation (47) have been obtained to date. The non-relativistic limit of (47) is, of course, equation (35) with n = 4.…”

Section: Two Three and Four-body Examplesmentioning

confidence: 99%

Section: Qed N-body Wave Equationsmentioning

confidence: 99%

See 1 more Smart Citation

RELATIVISTIC WAVE EQUATIONS OF n-BODY SYSTEMS OF FERMIONS AND ANTIFERMIONS OF VARIOUS MASSES IN QUANTUM ELECTRODYNAMICS

Emami-Razavi

Bergeron

Darewych

2012

Int. J. Mod. Phys. E

Self Cite

View full text Add to dashboard Cite

show abstract

“…The case of six-body system, for particles only and no virtual annihilation interaction [5], was done before and it has been included in the Tables 3 and 4 as well as the calculation of the case of combined three particles and three antiparticles with virtual annihilations and with retardation effects [9]. The corresponding graphs are also put in Fig.…”

Section: ð3:7þmentioning

confidence: 99%

“…In previous works by EmamiRazavi [5,6], it has been demonstrated that, by employing a reformulated model in QFT proposed by Darewych [7,8], formulas concerning relativistic n-body wave equations for scalar particles and/or antiparticles can be obtained (see also [9]). It has also been proven that using Darewych's formalism [7,8] relativistic n-fermion wave equations (particles and antiparticles; spin-1/2) in quantum electrodynamics can be obtained [10,11].…”

Section: Introductionmentioning

confidence: 99%

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

Self Cite

View full text Add to dashboard Cite

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.

show abstract

Energy momentum tensor on and off the light cone: exposition with scalar Yukawa theory

Cao,

Xu,

et al. 2024

J. High Energ. Phys.

View full text Add to dashboard Cite

We compute the gravitational form factors Ai, Di and $$ {\overline{c}}_i $$ c ¯ i of the scalar Yukawa theory using both the light-cone and covariant perturbation theory at the one-loop level. The light-cone formalism provides a potential approach to access these form factors beyond the perturbative regime. However, unlike the covariant formulation, the Poincaré symmetry on the light cone is not manifest. In this work, we use perturbation theory as a benchmark to extract the gravitational form factors from the light-front energy-momentum tensor. By comparing results on and off the light cone, we identify T++, T+a, T+−, T12 as the “good currents” that are properly renormalized and can be used to extract the gravitational form factors.

show abstract

Relativistic wave equations ofn-body systems of particles and antiparticles of various masses in scalar quantum field theory

Cited by 12 publications

References 51 publications

RELATIVISTIC WAVE EQUATIONS OF n-BODY SYSTEMS OF FERMIONS AND ANTIFERMIONS OF VARIOUS MASSES IN QUANTUM ELECTRODYNAMICS

RELATIVISTIC WAVE EQUATIONS OF n-BODY SYSTEMS OF FERMIONS AND ANTIFERMIONS OF VARIOUS MASSES IN QUANTUM ELECTRODYNAMICS

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

Energy momentum tensor on and off the light cone: exposition with scalar Yukawa theory

Contact Info

Product

Resources

About