Skip to main content
SpringerLink
Log in

Variational wave equations of two fermions interacting via scalar, pseudoscalar, vector, pseudovector and tensor fields

  • Published:
Central European Journal of Physics

Abstract

We consider a method for deriving relativistic two-body wave equations for fermions in the coordinate representation. The Lagrangian of the theory is reformulated by eliminating the mediating fields by means of covariant Green's functions. Then, the nonlocal interaction terms in the Lagrangian are reduced to local expressions which take into account retardation effects approximately. We construct the Hamiltonian and two-fermion states of the quantized theory, employing an unconventional “empty” vacuum state, and derive relativistic two-fermion wave equations. These equations are a generalization of the Breit equation for systems with scalar, pseudoscalar, vector, pseudovector and tensor coupling.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. M. Barham and J.W. Darewych: “Exact two-body eigenstates in scalar quantum field theory”, Journal of Physic A, Vol. 31, (1998), pp. 3481–3491.

    Article  MATH  MathSciNet  Google Scholar 

  2. J.W. Darewych and L. Di Leo: “Two-fermion Dirac-like eigenstates of the Coulomb QED Hamiltonian”, Journal of Physic A, Vol. 29, (1996), pp. 6817–6841.

    Article  MATH  Google Scholar 

  3. J.W. Darewych: “Few-particle eigenstates in the Yukawa model”, Condensed Matter Physics, Vol. 1, (1998), pp. 593–604.

    Google Scholar 

  4. J.W. Darewych and A. Duviryak: “Exact few-particle eigenstates in partially reduced QED”, Physical Review A, Vol. 66, (2002), pp. 032102

    Article  ADS  Google Scholar 

  5. G.V. Efimov: “Nonlocal quantum field theory and particle physics”, In: I.A. Batalin et al (Eds.):Quantum Field Theory and Quantum Statistics. Essays in honour of the sixtieth birthday of E.S. Fradkin, Adam Hilger, Bristol, pp. 545–564; G.V. Efimov:Problems of Quantum Theory of Nonlocal Interactions, Nauka, Moscow, 1985 (in Russian).

    Google Scholar 

  6. J. Kiskis: “Modified field theory for quark binding”, Physical Review D, Vol. 11, (1975), pp. 2178–2202.

    Article  ADS  Google Scholar 

  7. S. Blaha: “Embedding classical fields in quantum field theories”, Physical Review D, Vol. 17, (1978), pp. 994–1008.

    Article  MathSciNet  ADS  Google Scholar 

  8. L.L. Jenkovszky, F. Paccanoni and Z.E. Chikovani: “Gluon exchange in elastic hadron scattering”, Yadernaya Fizika, Vol. 53, (1991), pp. 526–538;Soviet Journal of Nuclear Physics, Vol. 53, (1991), pp. 329–336.

    Google Scholar 

  9. E.H. Kerner (Ed.):The Theory of Action-at-a-Distance in Relativistic Particle Mechanics, Collection of reprints, Gordon and Breach, New York, 1972.

    Google Scholar 

  10. P. Havas: “Galilei- and Lorentz-invariant particle systems and their conservation laws”, In: M. Bunge (Ed.).Problems in the Foundations of Physics, Springer, Berlin, 1971, pp. 31–48.

    Google Scholar 

  11. F. Hoyle and J.V. Narlicar:Action-at-a-Distance in Physics and Cosmology, Freeman and Co, San-Francisco, 1974.

    Google Scholar 

  12. V.N. Golubenkov and Ia.A. Smorodinskii: “Lagrangian function for the system of identical charged particles”, Zh. Eksp. Teor. Fiz., Vol. 31, (1956), p. 330;Soviet Physics. JETP, Vol. 4, (1957), p. 55.

    MATH  Google Scholar 

  13. L.D. Landau and E.M. Lifshitz:The Classical Theory of Fields, 4th rev. ed., Pergamon, New York, 1975.

    MATH  Google Scholar 

  14. B.M. Barker and R.F. O'Connell: “Acceleration-dependent lagrangians and equations of motion”, Physics Letters A, Vol. 78, (1980), pp. 231–232.

    Article  ADS  Google Scholar 

  15. B.M. Barker and R.F. O'Connell: “The post-post-Newtonian problem in classical electromagnetic theory”, Annals of Physics, NY, Vol. 129, (1980), pp. 358–377.

    Article  ADS  Google Scholar 

  16. G. Schäfer: “Acceleration-dependent lagrangians in general relativity”, Physics Letters A, Vol. 100, (1984), pp. 128–129.

    Article  ADS  Google Scholar 

  17. B.M. Barker and R.F. O'Connell: “Removal of acceleration terms from the two-body Lagrangian to orderc −4 in electromagnetic theory”, Canadian J. Phys., Vol. 58, (1980), pp. 1659–1666.

    MATH  MathSciNet  ADS  Google Scholar 

  18. R.P. Gaida, Yu.B. Kluchkovsky and V.I. Tretyak: “Three-dimensional Lagrangian approach to the classical relativistic dynamics of directly interacting particles”, In: G. Longhi and L. Lusanna (Eds.):Constraint's Theory and Relativistic Dynamics, Florence (Italy), 1986, World Scientific Publishing Co, Singapore, 1987, pp. 210–241.

    Google Scholar 

  19. R.W. Childers: “Effective Hamiltonians for generalized Breit interactions in QCD”, Physical Review D, Vol. 36, (1987), pp. 606–614.

    Article  ADS  Google Scholar 

  20. G. Breit: “The effect of retardation on the interaction of two electrons”, Physical Review, Vol. 34, (1929), pp. 553–573.

    Article  MATH  MathSciNet  ADS  Google Scholar 

  21. P. Van Alstine and H.W. Crater: “A tale of three equations: Breit, Eddington-Gaunt, and two-body Dirac”, Foundations of Physics, Vol. 27, (1997), pp. 67–79.

    MathSciNet  Google Scholar 

  22. G.D. Tsibidis: “Quark-Antiquark Bound States and the Breit Equation”, LANL e-Print archive (2000), http://xxx.lanl.gov/abs/hep-ph/0007143.

  23. D.D. Brayshaw: “Relativistic description of quarkonium”, Physical Review D, Vol. 36, (1987), pp. 1465–1478.

    Article  ADS  Google Scholar 

  24. I.V. Simenog and A.I. Turovsky: “A relativistic model of the two-nucleon problem with direct interaction”, Ukraïn. Fiz. Zh., Vol. 46, (2001), pp. 391–401 (in Ukrainian); I.V. Simenog and A.I. Turovsky: “The model of deuteron in Dirac-Breit approach with direct interaction”, Journal of Physical Studies, Vol. 8, (2004), pp. 23–34 (in Ukrainian).

    Google Scholar 

  25. A.A. Khelashvili: “Radial quasipotential equation for a fermion and antifermion and infinitely rising central potentials”, Teoreticheskaya i Matematicheskaya Fizika, Vol. 51, (1982), pp. 201–210;Theoretical and Mathematical Physics, Vol. 51, (1982), pp. 447–453.

    Google Scholar 

  26. H.W. Crater, C.W. Wong and C.-Y. Wong: “Singularity-free Breit equation from constraint two-body Dirac equations”, International Journal of Modern Physics E, Vol. 5, (1996), pp. 589–615.

    Article  ADS  Google Scholar 

  27. O. Mustafa and T. Barakat: “Nonrelativistic shifted-l expansion technique for three-and two-dimensional Schrödinger equation”, Communications in Theoretical Physics, Vol. 28, (1997), pp. 257–264; O. Mustafa and T. Barakat: “Relativistic shifted-l expansion technique for Dirac and Klein-Gordon equations”, Communications in Theoretical Physics, Vol. 29, (1998), pp. 587–594.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department for Metal and Alloy Theory, Institute for Condensed Matter Physics of the NAS of Ukraine, 1 Svientsitskii St., UA-79011, Lviv, Ukraine

    Askold Duviryak

  2. Department of Physics and Astronomy, York University, 4700 Keele St., M3J 1P3, Toronto, Ontario, Canada

    Jurij W. Darewych

Authors
  1. Askold Duviryak
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jurij W. Darewych
    View author publications

    You can also search for this author in PubMed Google Scholar

About this article

Cite this article

Duviryak, A., Darewych, J.W. Variational wave equations of two fermions interacting via scalar, pseudoscalar, vector, pseudovector and tensor fields. centr.eur.j.phys. 3, 467–483 (2005). https://doi.org/10.2478/BF02475607

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.2478/BF02475607

Keywords

PACS (2003)

Search

Navigation