Advertisement

Singularities in relativistic quantum mechanics

Conference paper
Part of the Lecture Notes in Mathematics book series (LNM, volume 209)

Keywords

Singular Point Feynman Rule Mass Shell Feynman Graph Internal Line 
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]
    W. Heisenberg, Die beobachtbären Grössen in der Theorie der Elementarteilchen. Zeitschrift für Physik 120 (1942), 513–538.MathSciNetCrossRefGoogle Scholar
  2. [2]
    R.P. Feynman, Space-time approach to quantum electrodynamics. Phys. Rev. 76 (1949), 769–789.MathSciNetCrossRefzbMATHGoogle Scholar
  3. [2a]
    , Mathematical formulation of the quantum theory of electromagnetic interaction. Phys. Rev. 80, (1950) 440–457.MathSciNetCrossRefzbMATHGoogle Scholar
  4. [3]
    F.J. Dyson, The S-matrix quantum electrodynamics. Phys. Rev. 75 (1949) 1736–1755.MathSciNetCrossRefzbMATHGoogle Scholar
  5. [4]
    L.D. Landau, On analytic properties of vertex parts in quantum field theory, Nuclear Phys. 13 (1959) 181–192.MathSciNetCrossRefzbMATHGoogle Scholar
  6. [5]
    P.V. Landshoff J.C. Polkinghorne and J.C. Taylor, A proof of the Mandestam representation in pertubation theory. Il Nuovo Cimento 19 (1961) 939–952.MathSciNetCrossRefzbMATHGoogle Scholar
  7. [6]
    S. Coleman and R.E. Norton, Singularities in the Physical Region. Il Nuovo Cimento 38 (1965) 438–442.CrossRefGoogle Scholar
  8. [7]
    M.J.W. Bloxham, D.I. Olive and J.C. Polkinghorne, S-matrix singularity structure in the physical region. I Properties of multiple integrals. J.Math. Phys: 10, (1969) 494–502.MathSciNetCrossRefzbMATHGoogle Scholar
  9. [8]
    R.E. Cutkosky, Singularities and discontinuities of Feynman amplitudes. J. Math. Phys. 1 (1960) 429–433.MathSciNetCrossRefzbMATHGoogle Scholar
  10. [9]
    M.J.W. Bloxham, D.I. Olive and J.C. Polkinghorne, S-matrix singularity structure in the physical region II Unitarity Integrals. J. Math. Phys. 10 (1969) 545–552.MathSciNetCrossRefGoogle Scholar
  11. [9a]
    , III General discussion of simple Landau singularities. J. Math. Phys. 10 (1969), 553–561.MathSciNetCrossRefGoogle Scholar
  12. [9b]
    J. Coster and H.P. Stapp, Physical Region Discontinuity Equations for Many-Particle Scattering Amplitudes I. J. Math. Phys. 10 (1969) 371–396.MathSciNetCrossRefGoogle Scholar
  13. [9c]
    , II. J. Math. Phys. 11 (1970) 1441–1463.MathSciNetCrossRefGoogle Scholar
  14. [10]
    F. Pham, Singularites des processus de diffusion multiple. Ann. Inst. Henri Poincare 6A (1967) 89–204.MathSciNetGoogle Scholar
  15. [11]
    F. Pham, in Symposia on Theoretical Physics vol.7 (Plenum, New York)Google Scholar
  16. [12]
    The manifold properties were also proved by: C. Chandler and H.P. Stapp, Macroscopic causality conditions and properties of scattering amplitudes. J. Math. Phys. 10 (1969) 826–859.MathSciNetCrossRefzbMATHGoogle Scholar
  17. [12a]
    C. Chandler, Causality in S-matrix theory. Phys. Rev. 174, (1968) 1749–1758.CrossRefGoogle Scholar
  18. [13]
    K. Symanzik, Dispersion relations and Vertex Properties in Perturbation Theory. Prog. Theor. Phys. 20 (1958), 690–702.MathSciNetCrossRefzbMATHGoogle Scholar
  19. [14]
    S. Mandelstam, Determination of the pion-nucleon scattering amplitude from dispersion relations and unitarity. General Theory. Phys. Rev. 112 (1958) 1344–1360.MathSciNetGoogle Scholar
  20. [15]
    R.J. Eden, P.V. Landshoff, J.C. Polkinghorne and J.C. Taylor, Acnodes and cusps on Landau curves. J. Math. Phys. 2 (1961) 656–663.MathSciNetCrossRefGoogle Scholar
  21. [16]
    G. Ponzano, T. Regge, E.R. Speer and M.J. Westwater, The monodromy rings of a class of self-energy graphs. Commun Math. Phys. 15 (1969), 83–132.MathSciNetCrossRefzbMATHGoogle Scholar
  22. [16a]
    T. Regge, p.433 in "Battelle Rencontres 1967" ed C.M. De Witt and J.A. Wheeler (W.A. Benjamin, New York 1968)Google Scholar
  23. [16b]
    T. Regge, in "Nobel Symposium 8: Elementary Particles Theory". ed Nils Svartholm (Interscience, New York, 1969).Google Scholar

Reference books

  1. [A]
    J.D. Bjorken and S.D. Drell, Relativistic quantum fields. McGraw-Hill, 1965.Google Scholar
  2. [B]
    N.N. Bogoliubov and D.V. Shirkov, Introduction to the Theory of Quantised Fields, Interscience, New York, 1959.Google Scholar
  3. [C]
    G.F. Chew, S-Matrix Theory of Strong Interactions. W.A. Benjamin, New York, 1961.Google Scholar
  4. [D]
    G.F. Chew, The Analytic S-Matrix. W.A. Benjamin, New York, 1966.Google Scholar
  5. [E]
    R.J. Eden, P.V. Landshoff, D.I. Olive, & J.C. Polkinghorne, The Analytic S-Matrix, Cambridge 1966.Google Scholar
  6. [F]
    R.P. Feynman, Quantum Electrodynamics. W.A. Benjamin, New York, 1962.zbMATHGoogle Scholar
  7. [G]
    R.C. Hwa and V.L. Teplitz, Homology and Feynman Integrals. W.A. Benjamin, New York, 1966.zbMATHGoogle Scholar
  8. [H]
    J.M. Jauch and F. Rohrlich, The Theory of Photons and Electrons. (Addison-Wesley, Cambridge, Mass., 1955.Google Scholar
  9. [I]
    F. Pham, Introduction a l’Etude Topologique des Singularites de Landau. Gauthier-Villars, Paris, 1967.zbMATHGoogle Scholar
  10. [J]
    S. Schweber, An Introduction to Relativistic Quantum Field Theory. Harper and Row, New York, 1961.Google Scholar
  11. [K]
    J. Schwinger, Quantum Electrodynamics. Dover, 1958.Google Scholar
  12. [L]
    I.T. Todorov, Analytic Properties of Feynman Graphs in Quantum Field Theory. Bulgarian Academy of Sciences, 1966. (To appear in English)Google Scholar

Copyright information

© Springer-Verlag Berlin · Heidelberg 1971

Authors and Affiliations

There are no affiliations available

Personalised recommendations