Advertisement

Atomic Physics and Quantum Electrodynamics in the Infinite Momentum Frame

  • Stanley J. Brodsky
Conference paper

Abstract

Over the past few years it has been shown that the use of an “infinite momentum” Lorentz frame1 has remarkable advantages for calculations in elementary particle physics and field theory, especially in the areas of current algebra sum rules,2 parton models, 3,4 and eikonal scattering.5,6 One important advantage is that it allows a straightforward application of the impulse and incoherence approximations familiar in nonrelativistic atomic and nuclear physics to relativistic field theory and bound state problems.

Keywords

Counter Term Lorentz Frame Feynman Amplitude Ladder Graph Vertex Insertion 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    S. Weinberg, Phys. Rev, 150, 1313 (1966). See also L. Susskind andG. Frye, Phys. Rev. 165, 1535 (1968); K. Bardakei and M. B. Halpern, Phys. Rev. 176, 1686 (1968).Google Scholar
  2. 2.
    S. Fubini and G. Furlan, Physics 1, 229 (1965); J. D. Bjorken, Phys. Rev. 179, 1547 (1969); R. Dashen and M. Gell-Mann, Phys. Rev. Letters 17, 340 (1966).Google Scholar
  3. 3.
    J. D. Bjorken and E. A. Paschos, Phys. Rev. 185, 1975 (1969).Google Scholar
  4. 4.
    S. D. Drell, D. J. Levy, and T. M. Yan, Phys, Rev. Letters 22, 744 (1969); Phys. Rev. 187, 2159 (1969); Phys. Rev. Dl, 1035 (1970); Phys. Rev. Dl, 1617 (1970). S. D. Drell and T. M. Yan, Phys. Rev. Dl, 2402 (1970); Phys. Rev. Letters 24, 181 (1970).Google Scholar
  5. 5.
    S. J. Chang and S. K. Ma, Phys. Rev. 180, 1506 (1969); 188, 2385 (1969).ADSCrossRefGoogle Scholar
  6. 6.
    J. B. Kogut and D. E. Soper, Phys. Rev. Dl, 2901 (1970); J. D. Bjorken, J. B. Kogut and D. E. Soper, Phys. Rev. D3, 1382 (1971).Google Scholar
  7. 7.
    C. M. Sommerfield, Phys. Rev. 107, 328 (1957); Ann. Phys. (N. Y.) 5, 26 (1958). A. Petermann, Helv. Phys. Acta 30, 407 (1957); Nueh Phys. 3, 689 (1957).Google Scholar
  8. 8.
    M. Levine and J. Wright, Phys. Rev. Letters 26, 1351 (1971); Proceedings of the Second Colloquium on Advanced Computing Methods in Theoretical Physics, Marseille (1971), and private communication.Google Scholar
  9. 9.
    S. Brodsky, R. Roskies, and R. Suaya (in preparation).Google Scholar
  10. 10.
    D. Foerster, University of Sussex preprint (1971). Foerster’s derivation of the lowest order anomalous moment a/2ir is particularly instructive. If the electron interacts with a magnetic field (transverse photon polarization), then one finds that the contribution of diagram 1(a) is negative (but logarithmic divergent) in agreement with Welton!s classical argument (T. Welton, Phys. Rev. 74, 1157 (1948)). The surviving Z-graph contribution of diagram 1(b) (and its mirror graph) is positive, cancels the divergent term, and leaves the finite a/2ir remainder. Note that diagram 1(b) contains the Thomson limit part of the Compton amplitude for the side-wise dispersion calculation of S. Drell and H0 Pagels, Phys. Rev. 140B, 397 (1965). The remaining diagrams vanish in the infinite momentum frame defined in Eq. (1).Google Scholar
  11. 11.
    The renormalization of the vertex insertions is generally algebraically more complicated, since, except for ladder graphs, the counter term must be rewritten to cancel the contributions of more than one time-ordering of the vertex. The procedure for this case is discussed in Ref. 9.Google Scholar
  12. 12.
    See, for example, S. J. Brodsky and J. D. Sullivan, Phys. Rev. 156, 1644 (1967).ADSCrossRefGoogle Scholar
  13. 13.
    All of the algebraic steps for our calculations were performed automatically using the algebraic computation program REDUCE, see A. C. Hearn, Stanford University preprint No. ITP-247 (unpublished); and A. C. Hearn in: Interactive Systems for Experimental Applied Mathematics, M. Klerer and J. Reinfields ( Academic Press, New York, 1968 ).Google Scholar
  14. 14.
    The numerical integrations were performed using the adaptive multidimensional integration program developed by C. Sheppey. See J. Aldins, S. Brodsky, A. Dufner, andT. Kinoshita, Phys. Rev. Dl, 2378 (1970); A. Dufner, Proceedings of the Colloquium on Computation Methods in Theoretical Physics (Marseille, 1970), and B. Lautrup, op. cit. (1971).Google Scholar
  15. 15.
    T. M. Yan and S. J. Chang, Cornell University preprints (1972).Google Scholar
  16. 16.
    G. Feldman, T. Fulton, and J. Townsend, John Hopkins University preprint (1972).Google Scholar
  17. 17.
    S. Brodsky, F. Close, and J. Gunion, Phys. Rev. D5, 1384 (1972).ADSGoogle Scholar
  18. 18.
    M. Goldberger and F. Low, Phys. Rev. 176, 1778 (1968).ADSCrossRefGoogle Scholar
  19. 19.
    J. Gunion, S. Brodsky, and R. Blankenbeeler, Report No. SLAC- PUB-1037 and Phys. Letters (to be published). For a discussion of atom-atom rearrangement collisions in potential theory, see K. M. Watson, in Atomic Physics, Proc0 of the First International Conference on Atomic Physics, 1968.Google Scholar

Copyright information

© Plenum Press, New York 1973

Authors and Affiliations

  • Stanley J. Brodsky
    • 1
  1. 1.Stanford Linear Accelerator CenterStanford UniversityStanfordUSA

Personalised recommendations