Skip to main content
SpringerLink
Log in

Volume dependence of the energy spectrum in massive quantum field theories

II. Scattering states

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

Abstract

The low-lying energy values associated to energy eigenstates describing two stable particles enclosed in a (space-like) box of sizeL are shown to be expandable in an asymptotic power series of 1/L. The coefficients in these expansions are related to the appropriate elastic scattering amplitude in a simple and apparently universal manner. At low energies, the scattering amplitude can thus be determined, if an accurate calculation of two-particle energy values is possible (by numerical simulation, for example).

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. Lüscher, M.: Volume dependence of the energy spectrum in massive quantum field theories, I. Stable particle states. Commun. Math. Phys.104, 177–206 (1986)

    Google Scholar 

  2. Lüscher, M.: On a relation between finite size effects and elastic scattering processes. In: Progress in gauge field theory. G.'t Hooft et al. (eds.) (Cargèse 1983). New York: Plenum Press 1984

    Google Scholar 

  3. Huang, K., Yang, C.N.: Quantum-mechanical many-body problem with hard-sphere interaction. Phys. Rev.105, 767 (1957)

    Google Scholar 

  4. Hamber, H.W., Marinari, E., Parisi, G., Rebbi, C.: Considerations on numerical analysis of QCD. Nucl. Phys. B225 [FS 9], 475 (1983)

    Google Scholar 

  5. Parisi, G.: The strategy for computing the hadronic mass spectrum. Phys. Rep.103, 203 (1984)

    Google Scholar 

  6. Gelfand, I.M., Shilov, G.E.: Generalized functions, Vol. 1. New York: Academic Press 1964

    Google Scholar 

  7. Dieudonné, J.: Foundations of modern analysis. New York: Academic Press 1969

    Google Scholar 

  8. Martin, B.R., Morgan, D., Shaw, G.: Pion-pion interactions in particle physics. New York: Academic Press 1976

    Google Scholar 

  9. Gasser, J., Leutwyler, H.: Chiral perturbation theory to one loop. Ann. Phys.158, 142 (1984)

    Google Scholar 

  10. Höhler, G., Kaiser, F., Koch, R., Pietarinen, E.: Handbook of pion-nucleon scattering. Physics Data 12-1, Fachinformationszentrum Karlsruhe (1979)

  11. Bethe, H.A., Morrison, Ph.: Elementary nuclear theory. New York: Wiley 1956

    Google Scholar 

  12. Münster, G.: The size of finite size effects in lattice gauge theories. Nucl. Phys. B249, 659 (1985)

    Google Scholar 

  13. Bros, J.:r-particle irreducible kernels, asymptotic completeness, and analyticity properties of several particle collision amplitudes. In: Mathematical Physics VII (Boulder 1983). Britten, W.E. et al. (eds.). Amsterdam: North-Holland 1984

    Google Scholar 

  14. Symanzik, K.: Continuum limit and improved action in lattice theories, I. Principles and φ4 theory. Nucl. Phys. B226, 187 (1983)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Theory Division, Deutsches Elektronen-Synchrotron DESY, D-2000, Hamburg 52, Federal Republic of Germany

    M. Lüscher

Authors
  1. M. Lüscher
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Communicated by G. Mack

Rights and permissions

Reprints and permissions

About this article

Cite this article

Lüscher, M. Volume dependence of the energy spectrum in massive quantum field theories. Commun.Math. Phys. 105, 153–188 (1986). https://doi.org/10.1007/BF01211097

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01211097

Keywords

Search

Navigation