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Unifying Many-Body Perturbation Theory with Quantum Electrodynamics

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Handbook of Relativistic Quantum Chemistry

Abstract

A unified procedure for many-body perturbation theory and quantum electrodynamics has been constructed by the Gothenburg group, based upon the recently developed covariant-evolution-operator method. This is a form of time- or energy-dependent perturbation theory, where all perturbations, including relativity and quantum electrodynamics, are built into the wave function, which is a necessary requisite for a true unification. The procedure is based upon the use of the Coulomb gauge, where the dominating part of the electron-electron interaction is expressed by means of the energy-independent Coulomb interaction and only the weaker energy-dependent transverse part by means of the covariant field theoretical expression. This leads to a more effective way of treating quantum electrodynamics in combination with electron correlation than the traditional purely quantum electrodynamical procedures. This will make it possible to go beyond two-photon exchange, which until now has been possible only for the lightest elements. The procedure has been implemented on highly charged helium-like ions.The procedure was primarily developed for static properties, but it is also applicable to dynamical processes, like scattering processes and electronic transition rates, as has recently been demonstrated.

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References

  1. Čársky P, Paldus J, Pittner J (eds) (2009) Recent progress in coupled cluster methods: theory and applications. Springer, New York

    Google Scholar 

  2. Mohr PJ, Plunien G, Soff G (1998) CODATA recommended values of the fundamental physical constants:2010. Phys Rep 293:227

    Article  CAS  Google Scholar 

  3. Shabaev VM (2002) Two-time Green’s function method in quantum electrodynamics of high-Z few-electron atoms. Phys Rep 356:119

    Article  CAS  Google Scholar 

  4. Lindgren I, Salomonson S, Åsén B (2004) The covariant-evolution-operator method in bound-state QED. Phys Rep 389:161

    Article  Google Scholar 

  5. Drake GWF (1988) Theoretical energies for the n = 1 and 2 states of the helium isoelectronic sequence up to Z=100. Can J Phys 66:586

    Article  CAS  Google Scholar 

  6. Drake GWF (2002) Progress in helium fine-structure calculations and the fine-structure constant. Can J Phys 80:1195

    Article  CAS  Google Scholar 

  7. Pachucki K (1999) Quantum electrodynamics effects on helium fine structure. J Phys B 32:137

    Article  CAS  Google Scholar 

  8. Pachucki K, Sapirstein J (2002) Determination of the fine structure constant from helium spectroscopy. J Phys B 35:1783

    Article  CAS  Google Scholar 

  9. Pachucki K (2006) Improved theory of Helium fine structure. Phys Rev Lett 97:013002

    Article  Google Scholar 

  10. Pachucki K, Yerokhin VA (2010) Reexamination of the helium fine structure. Phys Rev A 81:39903

    Article  Google Scholar 

  11. Plante DR, Johnson WR, Sapirstein J (1994) Relativistic all-order many-body calculations of the n=1 and n=2 states of heliumlike ions. Phys Rev A 49:3519

    Article  CAS  Google Scholar 

  12. Lindgren I, Salomonson S, Hedendahl D (2005) Many-body-QED perturbation theory: Connection to the two-electron Bethe-Salpeter equation. Einstein centennial review paper. Can J Phys 83:183

    Google Scholar 

  13. Lindgren I, Salomonson S, Hedendahl D (2006) Many-body procedure for energy-dependent perturbation: merging many-body perturbation theory with QED. Phys Rev A 73:062502

    Article  Google Scholar 

  14. Holmberg J, Salomonson S, Lindgren I (2015) Coulomb-gauge calculation of the combined effect of the correlation and QED for heliumlike highly charged ions. Phys Rev A 92:012509

    Article  Google Scholar 

  15. Lindgren I (2011) Relativistic many-body theory: a new field-theoretical approach. Springer, New York; Second revised edition (in production)

    Google Scholar 

  16. Lindgren I, Morrison J (1986) Atomic Many-Body Theory, 2nd edn. Springer, Berlin. Reprinted 2009

    Google Scholar 

  17. Lindgren I (1974) The Rayleigh-Schrödinger perturbation and the linked-diagram theorem for a multi-configurational model space. J Phys B 7:2441

    Article  CAS  Google Scholar 

  18. Bloch C (1958) Sur la théorie des perurbations des etats liés. Nucl Phys 6/7:329/451

    Google Scholar 

  19. Brueckner KA (1955) Many-Body Problems for Strongly Interacting Particles. II. Linked Cluster Expansion. Phys Rev 100:36

    CAS  Google Scholar 

  20. Goldstone J (1957) Derivation of the Brueckner many-body theory. Proc R Soc Lond Ser A 239:267

    Article  CAS  Google Scholar 

  21. Mukherjee D (1986) Linked-cluster theorem in the open-shell coupled-cluster theory for incomplete model spaces. Chem Phys Lett 125:207

    Article  CAS  Google Scholar 

  22. Lindgren I (1978) A coupled-cluster approach to the many-body perturbation theory for open-shell systems. Int J Quantum Chem S12:33

    Google Scholar 

  23. Lindgren I, Mukherjee D (1987) On the connectivity criteria in the open-shell coupled-cluster theory for the general model spaces. Phys Rep 151:93

    Article  CAS  Google Scholar 

  24. Bartlett RJ, Purvis GD (1978) Many-body perturbation theory, coupled-pair many-electron theory, and the importance of quadruple excitations for the correlation problem. Int J Quantum Chem 14:561

    Article  CAS  Google Scholar 

  25. Pople JA, Krishnan R, Schlegel HB, Binkley JS (1978) Electron correlation theories and their application to the study of simple reaction potential surfaces. Int J Quantum Chem 14:545

    Article  CAS  Google Scholar 

  26. Lindgren I, Salomonson S (1980) A numerical coupled-cluster procedure applied to the closed-shell atoms Be and Ne. Phys Scr 21:335

    Article  CAS  Google Scholar 

  27. Purvis GD, Bartlett RJ (1982) A full coupled-cluster singles and doubles model: the inclusion of disconnected triples. J Chem Phys 76:1910

    Article  CAS  Google Scholar 

  28. Löwdin P-O (1962) Studies in perturbation theory. V. Some aspects on the exact self-consistent field theory. J Math Phys 3:1171

    Google Scholar 

  29. Lindgren I (1985) Accurate many-body calculations on the lowest2 S and2 P states of the lithium atom. Phys Rev A 31:1273

    Article  CAS  Google Scholar 

  30. Grant IP (2007) Relativistic quantum theory of atoms and molecules. Springer, Heidelberg

    Book  Google Scholar 

  31. Sucher J (1980) Foundations of the relativistic theory of many electron atoms. Phys Rev A 22:348

    Article  CAS  Google Scholar 

  32. Kutzelnigg W (2012) Solved and unsolved problems in quantum chemistry. Chem Phys 395:16

    Article  CAS  Google Scholar 

  33. Liu W (2012) Perspectives of relativistic quantum chemistry: the negative energy cat smiles. Phys Chem Chem Phys 14:35

    Article  Google Scholar 

  34. Liu W, Lindgren I (2013) Going beyond ‘no-pair relativistic quantum chemistry’. J Chem Phys 139:014108

    Article  Google Scholar 

  35. Holmberg J (2011) Scalar vertex operator for bound-state QED in Coulomb gauge. Phys Rev A 84:062504

    Article  Google Scholar 

  36. Hedendahl D, Holmberg J (2012) Coulomb-gauge self-energy calculation for high-Z hydrogenic ions. Phys Rev A 85:012514

    Article  Google Scholar 

  37. Adkins G (1983) One-loop renormalization of Coulomb-gauge QED. Phys Rev D 27:1814

    Article  Google Scholar 

  38. Adkins G (1986) One-loop vertex function in Coulomb-gauge QED. Phys Rev D 34:2489

    Article  CAS  Google Scholar 

  39. Itzykson C, Zuber JB (1980) Quantum Field Theory. McGraw-Hill, New York

    Google Scholar 

  40. Lindgren I, Salomonson S, Hedendahl D (2010) In: Čársky P, Paldus J, Pittner J (eds) Recent progress in coupled cluster methods: theory and applications. Springer, New York, pp 357–374

    Chapter  Google Scholar 

  41. Hedendahl D (2010) Ph.D. thesis, University of Gothenburg, Gothenburg

    Google Scholar 

  42. Peskin ME, Schroeder DV (1995) An introduction to quantun field theory. Addison-Wesley Publ. Co., Reading

    Google Scholar 

  43. Chantler CT et al (2012) New X-ray measurements in Helium-like Atoms increase discrepancy between experiment and theoretical QED. arXiv-ph 0988193

    Google Scholar 

  44. Artemyev AN, Shabaev VM, Yerokhin VA, Plunien G, Soff G (2005) QED calculations of the n=1 and n=2 energy levels in He-like ions. Phys Rev A 71:062104

    Article  Google Scholar 

  45. Chantler CT (2012) Testing Three-Body Quantum-Electrodynamics with Trapped T20+ Ions: Evidence for a Z-dependent Divergence Between Experimental and Calculation. Phys Rev Lett 109:153001

    Article  CAS  Google Scholar 

  46. Kubic̆ek K, Mokler PH, Mäckel V, Ullrich J, López-Urrutia JC (2014) Transition energy measurements in hydrogenlike and heliumlike ions strongly supporting bound-state QED calculations. PRA 90:032508

    Google Scholar 

  47. Beiersdorfer P, Brown GV (2015) Experimental study of the X-ray transition in the helium like isoelectronic sequence: updated results. Phys Rev A 91:032514

    Article  Google Scholar 

  48. Epp SW et al (2015) Single-photon excitation of Kα in helium like Kr34+: Results supporting quantum electrodynamics predictions. Phys Rev A 92:020502(R)

    Google Scholar 

  49. Lindgren I, Salomonson S, Holmberg J (2014) QED effects in scattering involving atomic bound states: radiative recombination. Phys Rev A 89:062504

    Article  Google Scholar 

  50. Holmberg J, Salomonson S, Lindgren I (2015) Coulomb-gauge calculation of the combined effect of the correlation and QED for heliumlike highly charged ions. PRA 92:012509

    Article  Google Scholar 

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Acknowledgements

The author wants to express his gratitude to his coworkers Sten Salomonson and Johan Holmberg for their valuable collaboration and the latter also for making unpublished result available to him. The author also wants to acknowledge stimulating discussions with Professor Bogumil Jeziorski, Professor Werner Kutzelnigg, Professor Wenjian Liu, and Professor Debashis Mukherjee.

Author information

Authors and Affiliations

  1. Department of Physics, University of Gothenburg, Gothenburg, Sweden

    Ingvar Lindgren

  2. Laboratorie Kastler Brossel, UPMC-Sorbonne Universites, Collège de France and CNRS, Tour Zamanski, Bureau 2104, 4 Place Jussieu, 75233 Cedex 05, Paris, France

    Paul Indelicato

  3. PSL Research University, Tour Zamanski, Bureau 2104, 4 Place Jussieu, 75233 Cedex 05, Paris, France

    Paul Indelicato

Authors
  1. Ingvar Lindgren
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  2. Paul Indelicato
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Correspondence to Ingvar Lindgren .

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Editors and Affiliations

  1. Beijing National Laboratory for Molecular Sciences, Institute of Theoretical and Computational Chemistry, State Key Laboratory of Rare Earth Materials Chemistry and Applications, College of Chemistry and Molecular Engineering and Center for Computational Science and Engineering, Peking University, Beijing, China

    Wenjian Liu

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Lindgren, I., Indelicato, P. (2017). Unifying Many-Body Perturbation Theory with Quantum Electrodynamics. In: Liu, W. (eds) Handbook of Relativistic Quantum Chemistry. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-40766-6_29

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