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.
Similar content being viewed by others
References
Bach, V., Fröhlich, J., Sigal, I.M.: Quantum electrodynamics of confined non-relativistic particles. Adv. in Math. 137, 299–395 (1998)
Bach, V., Fröhlich, J., Sigal, I.M.: Renormalization group analysis of spectral problems in quantum field theory. Adv. in Math. 137, 205–298 (1998)
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)
Griesemer, M., Lieb, E., Loss, M.: Ground states in nonrelativistic quantum electrodynamics. Invent. Math. 145, 557–595 (2001)
Hiroshima, F.: Functional integral representation of a model in QED. Rev. Math. Phys. 9(4), 489–530 (1997)
Hiroshima, F.: Ground states of a model in nonrelativistic quantum electrodynamics II. J. Math. Phys. 41(2), 661–674 (2000)
Hiroshima, F., Spohn, H.: Ground state degeneracy of the Pauli-Fierz Hamiltonian with spin. Adv. Theor. Math. Phys. 5(6), 1091–1104 (2001)
Kato, T.: Perturbation Theory of Linear Operators, Volume 132 of Grundlehren der mathematischen Wissenschaften, 2nd ed., Berlin-Heidelberg-New York: Springer-Verlag, 1976
Lieb, E., Loss, M.: Existence of atoms and molecules in non-relativistic quantum electrodynamics. Adv. Theor. Math. Phys. 7(4), 667–710 (2003)
Pizzo, A.: One-particle (improper) states in Nelson's massless model. Ann. H. Poincaré 4(3), 439–486 (2003)
Reed, M., Simon, B.: Methods of Modern Mathematical Physics: Analysis of Operators. Volume 4, 1st ed., San Diego: Academic Press, 1978
Reed, M., Simon, B.: Methods of Modern Mathematical Physics: II. Fourier Analysis and Self-Adjointness. Volume 2, 2nd ed., San Diego: Academic Press, 1980
Author information
Authors and Affiliations
Corresponding author
Additional information
Communicated by G. Gallavotti
Rights 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
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00220-005-1478-3