Skip to main content
SpringerLink
Log in

Infrared-Finite Algorithms in QED: The Groundstate of an Atom Interacting with the Quantized Radiation Field

  • Published:
Communications in Mathematical Physics Aims and scope Submit manuscript

Abstract

In this paper, the groundstate of a nonrelativistic atom, minimally coupled to the quantized radiation field, and its groundstate energy are constructed by an iteration scheme inspired by [10]. This scheme successively removes an infrared cutoff in momentum space and yields a convergent algorithm enabling us to calculate the groundstate and the groundstate energy, to arbitrary order in the feinstructure constant α ~ 1/137. In forthcoming papers, we will use our result to re-expand the groundstate and, eventually, scattering amplitudes in terms of bare quantities.

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. Bach, V., Fröhlich, J., Sigal, I.M.: Quantum electrodynamics of confined non-relativistic particles. Adv. in Math. 137, 299–395 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  2. Bach, V., Fröhlich, J., Sigal, I.M.: Renormalization group analysis of spectral problems in quantum field theory. Adv. in Math. 137, 205–298 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  3. Bach, V., Fröhlich, J., Sigal, I.M.: Spectral analysis for systems of atoms and molecules coupled to the quantized radiation field. Commun. Math. Phys. 207(2), 249–290 (1999)

    Article  MathSciNet  Google Scholar 

  4. Griesemer, M., Lieb, E., Loss, M.: Ground states in nonrelativistic quantum electrodynamics. Invent. Math. 145, 557–595 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  5. Hiroshima, F.: Functional integral representation of a model in QED. Rev. Math. Phys. 9(4), 489–530 (1997)

    MathSciNet  Google Scholar 

  6. Hiroshima, F.: Ground states of a model in nonrelativistic quantum electrodynamics II. J. Math. Phys. 41(2), 661–674 (2000)

    Article  MathSciNet  Google Scholar 

  7. Hiroshima, F., Spohn, H.: Ground state degeneracy of the Pauli-Fierz Hamiltonian with spin. Adv. Theor. Math. Phys. 5(6), 1091–1104 (2001)

    MathSciNet  Google Scholar 

  8. Kato, T.: Perturbation Theory of Linear Operators, Volume 132 of Grundlehren der mathematischen Wissenschaften, 2nd ed., Berlin-Heidelberg-New York: Springer-Verlag, 1976

  9. Lieb, E., Loss, M.: Existence of atoms and molecules in non-relativistic quantum electrodynamics. Adv. Theor. Math. Phys. 7(4), 667–710 (2003)

    MathSciNet  Google Scholar 

  10. Pizzo, A.: One-particle (improper) states in Nelson's massless model. Ann. H. Poincaré 4(3), 439–486 (2003)

    Article  MathSciNet  Google Scholar 

  11. Reed, M., Simon, B.: Methods of Modern Mathematical Physics: Analysis of Operators. Volume 4, 1st ed., San Diego: Academic Press, 1978

  12. Reed, M., Simon, B.: Methods of Modern Mathematical Physics: II. Fourier Analysis and Self-Adjointness. Volume 2, 2nd ed., San Diego: Academic Press, 1980

Download references

Author information

Authors and Affiliations

  1. FB Mathematik, Universität Mainz, 55099, Mainz, Germany

    Volker Bach

  2. Inst. f. Theoretische Physik, ETH Hönggerberg, 8093, Zürich, Switzerland

    Jürg Fröhlich

  3. Dept. de Math, Univ. Paris-Sud, 91405, Orsay Cedex, France

    Alessandro Pizzo

  4. IHES, Bures-sur-Yvette, France

    Jürg Fröhlich

Authors
  1. Volker Bach
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jürg Fröhlich
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Alessandro Pizzo
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Volker Bach.

Additional information

Communicated by G. Gallavotti

Rights and permissions

Reprints and permissions

About this article

Cite this article

Bach, V., Fröhlich, J. & Pizzo, A. Infrared-Finite Algorithms in QED: The Groundstate of an Atom Interacting with the Quantized Radiation Field. Commun. Math. Phys. 264, 145–165 (2006). https://doi.org/10.1007/s00220-005-1478-3

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00220-005-1478-3

Keywords

Search

Navigation