Coupled Clusters and Quantum Electrodynamics

  • Ingvar LindgrenEmail author
  • Sten Salomonson
  • Daniel Hedendahl
Part of the Challenges and Advances in Computational Chemistry and Physics book series (COCH, volume 11)


We start by reviewing, as a background, the standard non-relativistic and relativistic many-body perturbative and coupled-cluster approaches in the way we have implemented them. The covariant-evolution-operator method that we introduced more recently for quantum-electrodynamical (QED) calculations is then described, and it is demonstrated how this method can be extended to combine electron-correlation and QED effects in a covariant manner. This can be included in a many-body calculation of coupled-cluster type, and it is demonstrated that this leads for two-particle systems eventually to the full Bethe–Salpeter equation. It is indicated how this procedure can also be applied to systems with more than two electrons. Preliminary numerical results are given for the ground state of some heliumlike ions.


Relativistic coupled cluster Quantum electrodynamics 


  1. 1.
    S. Fritzsche, P. Indelicato, T. Stö hlker, J. Phys. B38, S707 (2005)CrossRefGoogle Scholar
  2. 2.
    D. R. Plante, W. R. Johnson, J. Sapirstein, Phys. Rev. A49, 3519–3530 (1994)CrossRefGoogle Scholar
  3. 3.
    G. W. F. Drake, Can. J. Phys.66, 586–611 (1988)CrossRefGoogle Scholar
  4. 4.
    I. Lindgren, S. Salomonson, B. Åsén, Phys. Rep.389, 161–261 (2004)CrossRefGoogle Scholar
  5. 5.
    .K. A. Brueckner, Phys. Rev.100, 36–45 (1955)CrossRefGoogle Scholar
  6. 6.
    J. Goldstone, Proc. R. Soc. London, Ser. A239, 267–279 (1957)CrossRefGoogle Scholar
  7. 7.
    C. Bloch, Nucl. Phys.6/7, 329/451 (1958)CrossRefGoogle Scholar
  8. 8.
    B. H. Brandow, Rev. Mod. Phys.39, 771–828 (1967)CrossRefGoogle Scholar
  9. 9.
    I. Lindgren, J. Phys. B7, 2441–2470 (1974)CrossRefGoogle Scholar
  10. 10.
    F. Coster, Nucl. Phys.7, 421–424 (1958)CrossRefGoogle Scholar
  11. 11.
    H. Kü mmel, K. H. Lü hrman, J. G. Zabolitsky, Phys. Rep.36, 1–135 (1978)CrossRefGoogle Scholar
  12. 12.
    J. Čĺžek, J. Chem. Phys.45, 4256–4266 (1966)CrossRefGoogle Scholar
  13. 13.
    I. Lindgren, Int. J. Quantum Chem.S12, 33–58 (1978)Google Scholar
  14. 14.
    W. Ey, Nucl. Phys. A296, 189–204 (1978)CrossRefGoogle Scholar
  15. 15.
    D. Mukherjee, Chem. Phys. Lett.125, 207–212 (1986)CrossRefGoogle Scholar
  16. 16.
    I. Lindgren, D. Mukherjee, Phys. Rep.151, 93–127 (1987)CrossRefGoogle Scholar
  17. 17.
    I. Lindgren, J. Morrison, inAtomic Many-Body Theory, Second edition (Springer, Berlin, 1986, reprinted 2009)CrossRefGoogle Scholar
  18. 18.
    J. Sucher, Phys. Rev. A22, 348–362 (1980)CrossRefGoogle Scholar
  19. 19.
    H. Araki, Prog. Theor. Phys. (Japan)17, 619–642 (1957)CrossRefGoogle Scholar
  20. 20.
    J. Sucher, Phys. Rev.109, 1010–1011 (1957)CrossRefGoogle Scholar
  21. 21.
    J. Morrison, J. Phys. B6, 2205–2212 (1973)CrossRefGoogle Scholar
  22. 22.
    S. Garpman, I. Lindgren, J. Lindgren, J. Morrison, Phys. Rev. A11, 758–781 (1975)CrossRefGoogle Scholar
  23. 23.
    S. Garpman, I. Lindgren, J. Lindgren, J. Morrison, Z. Phys. A276, 167–177 (1976)CrossRefGoogle Scholar
  24. 24.
    I. Lindgren, J. Lindgren, A. M. Mårtensson, Z. Phys. A279, 113–125 (1976)CrossRefGoogle Scholar
  25. 25.
    A. M. Mårtensson, J. Phys. B12, 3995–4012 (1980)CrossRefGoogle Scholar
  26. 26.
    I. Lindgren, S. Salomonson, inA Numerical Coupled-Cluster Procedure Applied to the Closed-Shell Atoms Be and Ne. Presented at the Nobel Symposium on Many-Body Effects in Atoms and Solids, Lerum, 1979. Physica Scripta21, 335–342 (1980)Google Scholar
  27. 27.
    J. Morrison, S. Salomonson, inMany-Body Perturbation Theory of the Effective Electron–Electron Interaction for Open-Shell Atoms. Presented at the Nobel Symposium, Lerum, 1979. Physica Scripta21, 343–350 (1980)Google Scholar
  28. 28.
    S. Salomonson, I. Lindgren, A. M. Mårtensson, inNumerical Many-Body Perturbation Calculations on Be-like Systems Using a Multi-Configurational Model Space. Presented at the Nobel Symposium on Many-Body Effects in Atoms and Solids, Lerum, 1979. Physica Scripta21, 335–342 (1980)Google Scholar
  29. 29.
    I. Lindgren,Accurate many-body calculations on the lowest 2 S and2 P states of the lithium atom. Phys. Rev. A31, 1273–1286 (1985)CrossRefGoogle Scholar
  30. 30.
    S. Salomonson, P. Öster, Phys. Rev. A41, 4670–4681 (1989)CrossRefGoogle Scholar
  31. 31.
    S. Salomonson, A. Ynnerman, Phys. Rev. A43, 88–94 (1991)CrossRefGoogle Scholar
  32. 32.
    E. Lindroth, Phys. Rev. A37, 316–328 (1988)CrossRefGoogle Scholar
  33. 33.
    S. Salomonson, P. Öster, Phys. Rev. A40, 5548, 5559 (1989)CrossRefGoogle Scholar
  34. 34.
    S. A. Blundell, W. R. Johnson, Z. W. Liu, J. Sapirstein, Phys. Rev. A40, 2233–2246 (1989)CrossRefGoogle Scholar
  35. 35.
    E. Eliav, U. Kaldor, Y. Ishikawa, Phys. Rev. A50, 1121–1128 (1994)CrossRefGoogle Scholar
  36. 36.
    M. S. Safronova, J. Sapirstein, W. R. Johnson, Phys. Rev. A58, 1016–1028 (1998)CrossRefGoogle Scholar
  37. 37.
    R. Bukowski, B. Jeziorski, K. Szalewicz, J. Chem. Phys.110, 4165–4183 (1999)CrossRefGoogle Scholar
  38. 38.
    D. Hedendahl, S. Salomonson, I. Lindgren, Phys. Rev. (to be published) (2010)Google Scholar
  39. 39.
    A. L. Fetter, J. D. Walecka, inThe Quantum Mechanics of Many-Body Systems (McGraw-Hill, New York, 1971)Google Scholar
  40. 40.
    I. Lindgren, S. Salomonson, D. Hedendahl, inField-Theoretical Approach to Many-Body Perturbation Theory: Combining MBPT and QED. Invited talk at the Sixth International Conference of Computational Methods in Sciences and Engineering, Corfu, Greece, September 2007. Adv. Quantum Chem. (2008)Google Scholar
  41. 41.
    I. Lindgren, S. Salomonson, D. Hedendahl, Einstein centennial review paper. Can. J. Phys.83, 183–218 (2005)CrossRefGoogle Scholar
  42. 42.
    I. Lindgren, S. Salomonson, D. Hedendahl, Phys. Rev. A73, 062,502 (2006)CrossRefGoogle Scholar
  43. 43.
    I. Lindgren, H. Persson, S. Salomonson, L. Labzowsky, Phys. Rev. A51, 1167–1195 (1995)CrossRefGoogle Scholar
  44. 44.
    E. G. Myers, H. S. Margolis, J. K. Thompson, M. A. Farmer, J. D. Silver, M. R. Tarbutt, Phys. Rev. Lett.82, 4200–4203 (1999)CrossRefGoogle Scholar
  45. 45.
    T. R. DeVore, D. N. Crosby, E. G. Myers, Phys. Rev. Lett.100, 243,001 (2008)CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2010

Authors and Affiliations

  • Ingvar Lindgren
    • 1
    Email author
  • Sten Salomonson
    • 1
  • Daniel Hedendahl
    • 1
  1. 1.Department of PhysicsUniversity of GothenburgGothenburgSweden

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