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Orientation

  • Conference paper
Renormalization Theory

Part of the book series: NATO Advanced Study Institutes Series ((ASIC,volume 23))

Abstract

The purpose of this orientation is to provide an introduction to the detailed talks that follow. Renormalization theory is a notoriously complicated and technical subject. As a result it is easy to lose sight of the main themes in the welter of details. In the hope of making the theory more accessible to the earnest student, I shall not flinch from repeating things that all experts know. Furthermore, I hope and expect that many of the points I make will be repeated later; I have chosen them because I believe they are worth repeating.

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References

  1. M. Gell-Mann F. Low, Phys. Rev. 84 (1951) 350–4.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  2. P.T. Matthews and A. Salam, Nuovo Cimento 2 (1955) 120–134.

    Article  MathSciNet  MATH  Google Scholar 

  3. I.M. Gelfand A.M. Yaglom Integration in Functional Spaces and its Applications in Quantum Physics, Jour. Math. Phys. 1 (1960) 48–69.

    Article  ADS  Google Scholar 

  4. R.H. Cameron, Comm. in Pure and Applied Math (1960) 126–140.

    Google Scholar 

  5. C. DeWitt-Morette, Comm. in Math. Phys. 28 (1972) 47–67 and 37 (1974) 63–81.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  6. S. Albeverio R. Hoegh-Krohn, Mathematical Theory of Feyrman Path Integrals Oslo preprint 1974.

    Google Scholar 

  7. I.M. Gelfand and N.Ya. Vilenkin, Generalized Functions, Vol. 4, Academic Press 1964.

    Google Scholar 

  8. T. Nakano, Prog. Theoret Phys. 21 (1959) 241–59.

    Article  ADS  MATH  Google Scholar 

  9. J. Schwinger, Proc. Nat. Acad. Sci USA 44 (1958) 956–65.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  10. K. Symanzik, Euclidean Quantum Field Theory, pp. 153–226 in Local Quantum Theory, R. Jost Ed. Academic Press N.Y. (1969). This review contains references to earlier papers on Euclidean field theory.

    Google Scholar 

  11. E. Nelson, Jour. Funct. Analys. 12 (1973) 97–112.

    Article  MATH  Google Scholar 

  12. E. Nelson, A Quartic Interaction in Two Dimensions pp. 69–73 in Mathematical Theory of Elementary Particles Ed. R. Goodman I. Segal MIT Press, 1966.

    Google Scholar 

  13. J. Glimm A. Jaffe, phys. Rev. 176 (1968) 1945–51

    Article  MathSciNet  ADS  MATH  Google Scholar 

  14. J. Glimm A. Jaffe, Ann. Math. 91 (1970) 362–401

    Article  MathSciNet  MATH  Google Scholar 

  15. J. Glimm and A. Jaffe, Acta. Math. 125 (1970) 203–261.

    Article  MathSciNet  Google Scholar 

  16. F. Guerra, Phys. Rev. Letts 28 (1972) 1213–14.

    Article  ADS  Google Scholar 

  17. K. Osterwalder and R. Schrader, Comm. in Math. Phys. 31 (1973) 83–112 and 42 (1975) 281–305.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  18. K. Osterwalder, Euclidean Green’s Functions and Wightman Distributions, pp. 71–93 in Constructive Quantum Field Theory Lecture Notes in Phys. Vol. 25 Springer (1973).

    Article  ADS  Google Scholar 

  19. B. Simon The P(ø) 2 Euclidean (Quantum)Field Theory, Princeton Univ. Press (1974).

    Google Scholar 

  20. L. Breiman, Probability, Addison-Wesley, 1968.

    Google Scholar 

  21. T. Hida, Stationary Stochastic Processes, Princeton University Press 1970.

    MATH  Google Scholar 

  22. M. Reed, Functional Analysis and Probability Theory pp. 2–93 in Constructive Quantum Field Theory Lecture Notes in Phys. Vol. 25 Springer 1973.

    Article  ADS  Google Scholar 

  23. J. Cannon, Comm. in Math Phys. 35 (1974) 215–33.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  24. P. Collela O. Lanford, Sample Field Behavior for the Free Markov Random Field pp. 44–70 in Constructive Quantum Field Theory Lecture Notes in Phys. 25 Springer 1973.

    Article  ADS  Google Scholar 

  25. M. Reed and L. Rosen, Comm. in Math Phys. 36 (1974) 123–132.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  26. B. Simon J. Rosen, Duke Math. Jour. 42 (1975) 51–55.

    Article  MathSciNet  MATH  Google Scholar 

  27. S. Albeverio R. Hoegh-Krohn, Jour. Funct. Anal. 16 (1974) 39–82.

    Article  MathSciNet  MATH  Google Scholar 

  28. K. Osterwalder and R. Schräder, Helv. Phys. Acta. 46 (1973) 277–301.

    MathSciNet  Google Scholar 

  29. E. Seiler, Comm. in Math Phys. 42 (1975) 163–182.

    Article  MathSciNet  ADS  Google Scholar 

  30. I. Herbst, private communication.

    Google Scholar 

  31. J. Glimm and A. Jaffe, Fortschritte der Physik 21 (1973) 327–376.

    Article  MathSciNet  Google Scholar 

  32. A. Klein, Zeits. Wahrsch. Verw. Geb. 28 (1974) 323–34.

    Article  MATH  Google Scholar 

  33. S. Coleman, Phys. Rev. D11 (1975) 2088–97.

    Google Scholar 

  34. R. Haag and D. Kastler, Jour. Math. Phys. 5 (1964) 848–61.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  35. FJ.Dyson, Phys. Rev. 75 (1949) 486–502.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  36. FJ. Dyson, Phys. Rev. 75 (1949) 1736–55

    Article  MathSciNet  ADS  MATH  Google Scholar 

  37. J. Ward, Proc. Phys. Soc. Lond. A64 (1951) 54–6.

    Article  ADS  Google Scholar 

  38. JM. Jauch F. Rohrlich, Theory of Photons and Electrons, Addison Wesley (1955) Chapters 9 and 10.

    Google Scholar 

  39. T.T. Wu, Phys. Rev. 125 (1962) 1436–50 esp. p 1439.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  40. RL. Mills CN. Yang, Prog. Theoret. Phys. Supp. 37 (1966) 507–511.

    Article  ADS  Google Scholar 

  41. A. Salam, Phys. Rev. 82 (1951) 217–227 and 84 (1951) 426–431.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  42. P.T. Matthews and A. Salam, Rev. Mod. Phys. 23 (1951) 311–4.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  43. S. Weinberg, Phys. Rev. 118 (1960) 838–49

    Article  MathSciNet  ADS  MATH  Google Scholar 

  44. JD. Bjorken S. Drell, Relativistic Quantum Fields, McGraw Hill (1965) chapter 19.

    MATH  Google Scholar 

  45. R. Johnson, J. Math. Phys. 11 (1970) 2161–5

    Article  ADS  Google Scholar 

  46. K. Symanzik, Green’s Functions Method and Renormalization of Renormalizable Quantum Field Theories, pp. 485–517 in Lecture on High Energy Physics II, Hercegnovi. 1961, Ed. B. Jakśić.

    Google Scholar 

  47. ECG. Stueckelberg TA. Green, Helv.Phys. Acta.24 (1951) 153–174.

    MathSciNet  MATH  Google Scholar 

  48. N.Bogoliubov D. Shirkov, Introduction to the Theory of Quantized Fields, New York Interscience, 1959.

    Google Scholar 

  49. N. Bogoliubov O. Parasiuk, Acta. Math. 97 (1957) 227–266.

    Article  MathSciNet  Google Scholar 

  50. N. K. Hepp, Comm. in Math Phys. 2 (1966) 301–26.

    Article  ADS  MATH  Google Scholar 

  51. M. Riesz, Acta. Math. 81 (1948) 1–223 and earlier references quoted there.

    Article  MathSciNet  Google Scholar 

  52. SB. Nilsson, Arkiv Fysik 1 (1950) 369–423 and earlier work quoted there.

    Google Scholar 

  53. E. Karlson, Arkiv für Fysik 7 (1953) 221–37.

    MathSciNet  Google Scholar 

  54. C. Bollini, J. Giambiagi and A. Dominguez, Nuovo Cim. 31 (1964) 550–61.

    Article  Google Scholar 

  55. E. Speer, Generalized Feynman Amplitudes, Annals of Math. Study No. 62 Princeton Press, 1969.

    Google Scholar 

  56. K. Hepp, Comm. in Math. Phys. 14 (1969) 67–9.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  57. G. ’t Hooft and M. Veltman, Nuclear Physics B44 (1972) 189–213.

    Article  MathSciNet  Google Scholar 

  58. O. Steinmann, Perturbation Expansions in Axiomatic Field Theory Lecture Notes in Physics 11 J. Springer (1971).

    Google Scholar 

  59. H. Epstein and V. Glaser, Ann. Inst. H. Poincare 19 (1973) 211–95.

    MathSciNet  Google Scholar 

  60. P. Blanchard and R. Seneor, Ann. Inst. H. PoincaJre, to appear.

    Google Scholar 

  61. K. Hepp, Renormalization Theory pp. 429–500 in Statistical Mechanics and Quantum Field Theory Ed. C. DeWitt and R. Stora Gordon and Breach, 1971.

    Google Scholar 

  62. S. Coleman, Secret Symmetry: An Introduction to Spontaneous Symmetry Breakdown and Gauge Fields in Proceedings of the 1973 School Ettore Majorana.

    Google Scholar 

  63. J. Bernstein, Rev. Mod. Phys. 46 (1974) 7–48.

    Article  ADS  Google Scholar 

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Author information

Authors and Affiliations

  1. Princeton University, Princeton, N.J, USA

    A. S. Wightman

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  1. A. S. Wightman
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Editor information

Editors and Affiliations

  1. International School of Mathematics Physics, Bologna, Italy

    G. Velo

  2. Dept. of Physics, Princeton University, Princeton, N.I., USA

    A. S. Wightman

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© 1976 D. Reidel Publishing Company, Dordrecht-Holland

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Wightman, A.S. (1976). Orientation. In: Velo, G., Wightman, A.S. (eds) Renormalization Theory. NATO Advanced Study Institutes Series, vol 23. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-1490-8_1

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  • DOI: https://doi.org/10.1007/978-94-010-1490-8_1

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-1492-2

  • Online ISBN: 978-94-010-1490-8

  • eBook Packages: Springer Book Archive

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