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Introduction to the physical applications of invariant wave equations

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Book cover Invariant Wave Equations

Part of the book series: Lecture Notes in Physics ((LNP,volume 73))

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References

  1. P.A.M. Dirac, Relativistic Wave Equations, Proc.Roy.Soc.Lond. 155A (1936) 447–459.

    Google Scholar 

  2. M. Fierz, Über die relativistische Theorie kraftfreier Teilchen mit beliebigem Spin, Helv. Phys. Acta 12 (1939) 3–37.

    Google Scholar 

  3. M. Fierz and W. Pauli, On Relativistic Waves Equations for Particles of Arbitrary Spin in an Electromagnetic Field, Proc. Roy. Soc. Lond. 173A (1939) 211–232.

    Google Scholar 

  4. G. Wentzel, Quantum Field Theory, p.205, Wiley-Interscience, New York, (1969).

    Google Scholar 

  5. P. Federbush, Minimal Electromagnetic Coupling for Spin Two Particles, Nuovo Cimento 19 (1961) 512–513.

    Google Scholar 

  6. J. W. Weinberg, Univ. Cal. Berkeley Thesis, Studies in the Quantum Field Theory of Elementary Particles, 1943 unpublished. S. Kusaka and J. W. Weinberg, Charged Particles of Higher Spin unpublished.

    Google Scholar 

  7. E. Wild, On first order waves equations for elementary Particles without subsidiary conditions, Proc.Roy.Soc.Lond. 191A (1947) 253–268.

    Google Scholar 

  8. K. Johnson and E. Sudarshan, The Impossibility of a Consistent Theory of Charged Higher Spin Fermi Fields, Ann. of Phys. 13 (1961) 126–145.

    Google Scholar 

  9. For a review of developments up to the end of the 1940's see E. M. Corson, Introduction to Tensors, Spinors, and Relativistic Wave Equations, Blackie, London 1953.

    Google Scholar 

  10. G. Velo and D. Zwanziger, Propagation and Quantization of Rarita-Schwinger Waves in an External Electromagnetic Potential, Phys. Rev. 186 (1969) 1337–1341.

    Google Scholar 

  11. G. Velo and D. Zwanziger, Non causality and other defects of Interaction Lagrangians for Particles with Spin 1 and Higher, Phys. Rev. 188 (1969) 2218–2222.

    Google Scholar 

  12. A. Capri, Electron in a Given Time Dependent Electromagnetic Field, J. Math. Phys. 10 (1969) 575–580.

    Google Scholar 

  13. A. S. Wightman, Partial Differential Equations and Relativistic Quap-tum Field Theory, Lectures in Differential Equations, Vol.II, A. K. Aziz Editor, van Nostrand, Princeton New Jersey 1969.

    Google Scholar 

  14. A. S. Wightman, Relativistic Wave Equations as Singular Hyperbolic Systems, pp. 441–477 in Partial Differential Equations, Proceedings of Symposia in Pure Math., Vol. XXIII, Amer. Math. Soc., Providence, Rhode Island 1973.

    Google Scholar 

  15. G. Velo, Anomalous Behavior of a Massive Spin Two Charged Particle in an External Electromagnetic Field, Nuclear Physics B43 (1972) 389–401.

    Google Scholar 

  16. G. Velo, An Existence Theorem for a Massive Spin One Particle in an External Tensor Field, Annales de l'Institut Henri Poincaré 22, (1975) 249–255.

    Google Scholar 

  17. G. Iversen, Some Remarks on the Supermultiplet Theory, pp. 44–64 in Troubles in the External Field Problem, Tracts in Mathematical and Natural Sciences, Vol. 4, Gordon and Breach 1971.

    Google Scholar 

  18. W. J. Hurley, Relativistic Wave Equations for Particles with Arbitrary Spin, Phys. Rev. D4 (1971) 3605–3616.

    Google Scholar 

  19. W. J. Hurley, Consistent Description of Higher Spin Fields, Phys. Rev. Letts. 29 (1972) 1475–1477.

    Google Scholar 

  20. W. J. Hurley, Invariant Bilinear Forms and the Discrete Symmetries for Relativistic Arbitrary Spin Fields, Phys. Rev. D10 (1974) 1185–1200

    Google Scholar 

  21. R. A. Krajcik and M. M. Nieto, Bhaba First Order Wave Equations I...VIII, Part VII is Phys. Rev. D15 (1977) 445–452; it contains references to the six earlier papers.

    Google Scholar 

  22. R. A. Krajcik and M. M. Nieto, Foldy Wouthuysen Transformations in an Indefinite Metric Space I... IV, part IV is Phys. Rev. D15 (1977) 426–432

    Google Scholar 

  23. A. Wightman, Instability Phenomena in the External Field Problem for Two Classes of Relativistic Wave Equations, pp.423–460 in Studies in Mathematical Physics, Essays in Honor of Valentine Bargmann, eds. E. Lieb, B. Simon, A. Wightman, Princeton Press 1976.

    Google Scholar 

  24. S. Deser and B. Zumino, Broken Super Symmetry and Super Gravity, Physics Letts. 38 (1977) 1433–1436.

    Google Scholar 

  25. T. Nakano, Quantum Field Theory in Terms of Euclidean Parameters, Prog. Theor. Phys. 21 (1959) 241–259.

    Google Scholar 

  26. J. Schwinger, On the Euclidean Structure of Relativistic Quantum Field Theory, Proc. Nat-Acad. Sci. U. S. A. 44 (1958) 956–965.

    Google Scholar 

  27. E. Nelson, Construction of Quantum Fields from Markoff Fields, Jour. Fcnal. Anal. 12 (1973) 97–112.

    Google Scholar 

  28. K. Osterwalder and R. Schrader, Axioms for Euclidean Green's Functions Commun. Math. Phys. 31 (1973) 83–112, II ibid 42 (1975) 281-305; T K. Osterwalder, Euclidean Green's Functions and Wightman Distributions, pp.71-93 in Constructive Quantum Field Theory, Lecture Notes in Physics # 25 Springer Verlag Berlin 1973, eds. G. Velo and A. Wightman.

    Google Scholar 

  29. The following account of the Euclidean Gell-Mann-Low formula is deliberately abbreviated since the preceding school of mathematical physics treated the matter in some detail. See, in particular [30], [31].

    Google Scholar 

  30. E. Seiler, Non Perturbative Renormalization in the Yukawa Model in Two Dimensions pp 415–433 Renormalizarion Theory eds. G. Velo and A. Wightman, D. Reidel Dordrecht Holland 1976, serves as an introduction to the papers: E. Seiler Schwinger Functions for the Yukawa Model in Two Dimensions with Space-Time Cutoff Commun. Math. Phys. 42 (1975) 163–182

    Google Scholar 

  31. B. Simon On Finite Mass Renormalizations in the Two Dimensional Yukawa Model Jour. Math. Phys. 16 (1975) 2289–2293.

    Google Scholar 

  32. E. Seiler and B. Simon Bounds in the Yukawa Quantum Field Theory Upper Bound on the Pressure, Hamiltonian Bound and Linear Lower Bound Commun. Math. Phys. 45 (1975) 99–114.

    Google Scholar 

  33. E. Seiler and B. Simon Nelson's Symmetry and All That in the Y 2 and (ø4 3 Quantum Field Theories, Annals of Physics 97 (1976) 420–518.

    Google Scholar 

  34. O. McBryan, Finite Mass Renormalizations in the Euclidean Yukawa 2 Field Theories, Commun. Math. Phys. 44 (1975) 237–243.

    Google Scholar 

  35. O. McBryan, Volume Dependence of Schwinger Functions in the Yukawa 2 Quantum Field Theory, Commun. Math. Phys. 45 (1975) 279–294.

    Google Scholar 

  36. O. McBryan, Convergence of the Vacuum Energy Density,-Bounds and Existence of Wightman Functions for the Yukawa 2 Model pp.237–252 in Les Méthodes Mathématiques de la Théorie Quantique des Champs, 1975.

    Google Scholar 

  37. A. S. Wightman, Orientation pp.1–24 in Renorm alization Theory, Proceedings of the NATO Advanced Study Institute held at Erice 1975, eds. G. Velo and A. S. Wightman, D. Reidel Dordrecht Holland 1976.

    Google Scholar 

  38. M. C. Reed, Functional Analysis and Probability Theory, pp. 2–43 and P. Colella and O. Lanford, Appendix: Sample Field Behavior for the Free Markov Random Field pp. 44–70 in Constructive Quantum Field Theory.

    Google Scholar 

  39. I learned it from K. Symanzik in the early 1960's. See Green's Functions and the Quantum Theory of Fields pp 490–531 in Lectures in Theoretical Physics III, Boulder 1960, ed. W. Britten, et al-Interscience Publishers N. Y. 1961. There it is derived for the generating functional of the Green's functions.

    Google Scholar 

  40. J. Fröhlich, New Super-Selection Sectors (“Soliton States”) in Two Dimensional Bose Quantum Field Theory Models, Comm. Math. Phys. 47 (1976) 269–310.

    Google Scholar 

  41. J. Fröhlich, Phase Transitions, Goldstone Bosons and Topological Super Selection Rules, Acta Physica Austriaca Suppl. XV (1976) 133–269.

    Google Scholar 

  42. In addition to the lectures of Gervais, I would recommend S. Coleman Classical Lumps and their Quantum Descendents, Erice Lectures 1975, for a general account of this subject.

    Google Scholar 

  43. J. Bellissard and R. Seiler, On the Fierz-Pauli Equation for Particles with Spin 3/2, Lett. al Nuovo Cimento 5 (1972) 221–225.

    Google Scholar 

  44. A. S. Wightman, The Dirac Equation, pp 95–115 in Aspects of Quantum theory, eds. A. Salam and E. P. Wigner, Cambridge University Press London, 1972 p.105.

    Google Scholar 

  45. G. Vélo, Restrictions on the Interactions between Vector Mesons, Nuclear Physics B65 (1973) 427–444.

    Google Scholar 

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Authors
  1. A. S. Wightman
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Giorgio Velo Arthur S. Wightman

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© 1978 Springer Verlag

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Wightman, A.S. (1978). Introduction to the physical applications of invariant wave equations. In: Velo, G., Wightman, A.S. (eds) Invariant Wave Equations. Lecture Notes in Physics, vol 73. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0032328

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  • DOI: https://doi.org/10.1007/BFb0032328

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  • Print ISBN: 978-3-540-08655-0

  • Online ISBN: 978-3-540-35929-6

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