Skip to main content
Log in

Uniqueness of the Ground State in the Feshbach Renormalization Analysis

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

Abstract

In the operator theoretic renormalization analysis introduced by Bach, Fröhlich, and Sigal, we prove uniqueness of the ground state.

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

Access this article

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

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Bach V., Chen T., Fröhlich J., Sigal I.M.: Smooth Feshbach map and operator-theoretic renormalization group methods. J. Funct. Anal. 203, 44–92 (2003)

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  3. Bach V., Fröhlich J., Sigal I.M.: Quantum electrodynamics of confined nonrelativistic particles. Adv. Math. 137(2), 209–395 (1998)

    Google Scholar 

  4. Chen T.: Infrared renormalization in non-relativistic QED and scaling criticality. J. Funct. Anal. 254, 2555–2647 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  5. Fröhlich J., Griesemer M., Sigal I.M.: On spectral renormalization group. Rev. Math. Phys. 21(4), 511–548 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  6. Griesemer M., Lieb E., Loss M.: Ground states in non-relativistic quantum electrodynamics. Invent. Math. 145(3), 557–595 (2001)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  7. Griesemer M., Hasler D.: On the smooth Feshbach-Schur Map. J. Funct. Anal. 254, 2329–2335 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  8. Griesemer M., Hasler D.: Analytic perturbation theory and renormalization analysis of matter coupled to quantized radiation. Ann. Henri Poincaré 10(3), 577–621 (2009)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  9. Hasler D., Herbst I.: Ground state properties of the spin boson model. Ann. Henri Poincaré 12, 621–677 (2011)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  10. Hasler, D., Herbst, I.: Convergent expansions in non-relativistic QED: analyticity of the ground state. J. Funct. Anal. arXiv:1005.3522 (to appear)

  11. Hasler, D., Herbst, I.: Smoothness and analyticity of perturbation expansions in QED. Adv. Math. arXiv:1007.0969 (to appear)

  12. Hiroshima F., Spohn H.: Two-fold degeneracy of the ground state band for the Pauli–Fierz model with spin. Adv. Theor. Math. Phys. 5, 1091–1104 (2002)

    MathSciNet  Google Scholar 

  13. Sigal I.M.: Ground state and resonances in the standard model of the non-relativistic QED. J. Stat. Phys. 134(5–6), 899–939 (2009)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  14. Spohn H.: Dynamics of Charged Particles and their Radiation Field. Cambridge University Press, Cambridge (2004)

    Book  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Ira Herbst.

Additional information

David Hasler: on leave from Ludwig Maximilians University, Munich.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Hasler, D., Herbst, I. Uniqueness of the Ground State in the Feshbach Renormalization Analysis. Lett Math Phys 100, 171–180 (2012). https://doi.org/10.1007/s11005-011-0532-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11005-011-0532-7

Mathematics Subject Classification (2010)

Keywords

Navigation