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Two-Time Greens Function Method

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Handbook of Relativistic Quantum Chemistry

Abstract

In this chapter we describe the Two-Time Greens Function (TTGF) method developed by V. M. Shabaev. This method allows derivation of the formulas for the energy shift and other QED effects. Unlike the preceeding methods, the TTGF one is suitable not only in the case of single isolated, but also for the (quasi-)degenerate levels. Starting from the very basic principles and concepts of QED, we will demonstrate, how to derive basic formulas with the help of TTGF method and apply them to the case of many-electron systems.

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References

  1. Dirac PAM (1928) The quantum theory of the electron. Proc R Soc Lond Ser A 117(778):610

    Article  Google Scholar 

  2. Feynman RP (1949) Space-time approach to quantum electrodynamics. Phys Rev 76:769

    Article  Google Scholar 

  3. Gell-Mann M, Low F (1951) Bound states in quantum field theory. Phys Rev 84(2):350

    Article  CAS  Google Scholar 

  4. Sucher J (1957) S-Matrix formalism for level-shift calculations. Phys Rev 107(5):1448

    Article  CAS  Google Scholar 

  5. Braun MA, Gurchumelia AD (1980) Relativistic adiabatic perturbation theory for degenerate levels. Theor Math Phys 45:199

    Article  Google Scholar 

  6. Braun MA, Gurchumelia AD, Safronova UI (1984) Relativistic thory of atom. Nauka, Moscow

    Google Scholar 

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

    Article  CAS  Google Scholar 

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

    Article  Google Scholar 

  9. Andreev OY, Labzowsky LN, Plunien G, Solovyev DA (2008) QED theory of the spectral line profile and its applications to atoms and ions. Phys Rep 455:135

    Article  CAS  Google Scholar 

  10. Artemyev AN, Shabaev VM, Tupitsyn II, Plunien G, Yerokhin VA (2007) QED Calculation of the 2p 3∕2 − 2p 1∕2 transition energy in boronlike argon. Phys Rev Lett 98(17):173004

    Article  Google Scholar 

  11. Artemyev AN, Shabaev VM, Tupitsyn II, Plunien G, Surzhykov A, Fritzsche S (2013) Ab initio calculations of the 2p 3∕2 − 2p 1∕2 fine-structure splitting in boronlike ions. Phys Rev A 88:032518. 10.1103/PhysRevA.88.032518, http://link.aps.org/doi/10.1103/PhysRevA.88.032518

    Article  Google Scholar 

  12. Itzykson C, Bernard Zuber J (1980) Quantum field theory. McGraw-Hill, New York

    Google Scholar 

  13. Bjorken JD, Drell SD (1964) Relativistic quantum mechanics. McGraw-Hill, New York

    Google Scholar 

  14. Szökefalvi-Nagy B (1946/1947) Perturbations des transformations autoadjointes dans l’espace de Hilbert. Comment Math Helv 19:347 (in French)

    Google Scholar 

  15. Kato T (1949) On the convergence of the perturbation method. Prog Theor Phys 4:514

    Article  Google Scholar 

  16. Kato T (1966) Perturbation theory for linear operators. Die Grundlagen der mathematischen Wissenschaften in Einzeldarstellungen, vol 132. Springer, New York

    Book  Google Scholar 

  17. Messiah A (1961) Quantum mechanics, vol 2. North-Holland, Amsterdam

    Google Scholar 

  18. Lepage GP (1977) Analytic bound-state solutions in a relativistic two-body formalism with applications in muonium and positronium. Phys Rev A 16(3):863

    Article  CAS  Google Scholar 

  19. Shabaev VM (1988) In: Safronova UI (ed) Many-particle effects in atoms. AN SSSR, Nauchnyi Sovet po Spektroskopii, Moscow), p 15

    Google Scholar 

  20. 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 

  21. Shabaev VM (1994) Quantum electrodynamic theory of recombination of an electron with a highly charged ion. Phys Rev A 50(6):4521

    Article  CAS  Google Scholar 

  22. Shabaev VM (1993) Schrödinger-like equation for the relativistic few-electron atom. J Phys B 26:4703

    Article  CAS  Google Scholar 

  23. Mittleman MH (1972) Configuration-space Hamiltonian for heavy atoms and correction to the Breit interaction. Phys Rev A 5:2395

    Article  Google Scholar 

  24. 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 

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Acknowledgements

Stimulating discussions with Prof. V. M. Shabaev and Prof. P. Indelicato are gratefully acknowledged.

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Artemyev, A. (2017). Two-Time Greens Function Method. In: Liu, W. (eds) Handbook of Relativistic Quantum Chemistry. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-40766-6_28

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