Skip to main content
SpringerLink
Log in
Book cover

Unified Theories of Elementary Particles pp 117–136Cite as

Spontaneously broken and dynamically enhanced global and local symmetries

  • Conference paper
  • First Online:

Part of the book series: Lecture Notes in Physics ((LNP,volume 160))

Abstract

I re-examine the notions of spontaneously broken, global and local symmetries and discuss them in terms of some examples in quantum field theory or statistical mechanics. I then briefly recall some basic ideas and facts about the renormalization group. They are used to introduce and discuss the concept of dynamically enhanced (or “generated”) asymptotic symmetries.

This is a preview of subscription content, log in via an institution.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References.

  1. H. Weyl,“Symmetry”, Princeton, N.J.: Princeton University Press, 1952.

    Google Scholar 

  2. S. Coleman, Secret Symmetry: An Introduction to Spontaneous Symmetry Breakdown and Gauge Fields, Erice Lectures 1973, A. Zichichi (ed.).

    Google Scholar 

  3. J. Fröhlich, Bull. Amer. Math. Soc. 84, 165, (1978).

    Google Scholar 

  4. L. Michel, Reviews of Modern Physics 52, 617, (1980).

    Google Scholar 

  5. J. Goldstone, Nuovo Cimento 19, 15, (1961); Y. Nambu and G. Jona-Lasinio, Phys. Rev. 122, 345, (1961), 124, 246, (1961).

    Google Scholar 

  6. H. Ezawa and J.A. Swieca, Commun. math. Phys. 5, 330, (1967).

    Google Scholar 

  7. J. Fröhlich, B. Simon and T. Spencer, Commun. math. Phys. 50, 79, (1976).

    Google Scholar 

  8. J. Fröhlich and T. Spencer, in “New Developments in Quantum Field Theory and Statistical Mechanics”, M. Lévy and P. Mitter (eds.), New York & London: Plenum, 1977.

    Google Scholar 

  9. J. Fröhlich, Acts, Physics Austrica Suppl. XV, 133, (1976).

    Google Scholar 

  10. S. Elitzur, Phys. Rev. D12, 3978, (1975).

    Google Scholar 

  11. G.F. De Angelis, D. De Falco and F. Guerra, Phys. Rev. D17, 1624, (1978).

    Google Scholar 

  12. J. Fröhlich, G. Morchio and F. Strocchi, Phys. Letts. 97B, 249, (1980); Nucl. Phys. B, in press.

    Google Scholar 

  13. K. Wilson and J. Kogut, Physics Reports 12C, No2, 76, (1974).

    Google Scholar 

  14. K. Wilson, Rev. Mod. Phys. 47, No4

    Google Scholar 

  15. L. Kadanoff, A. Haughton and M. Yalabik, J. Stat. Phys. 14, No2, 171, (1976).

    Google Scholar 

  16. G. Jona-Lasinio, Nuovo Cimento 26B,99, (1975).

    Google Scholar 

  17. S. Ma, Rev. Mod. Phys. 46, No4, 589, (1973).

    Google Scholar 

  18. P. Bleher and Ja. Sinsi, Commun. math. Phys. 33, 23, (1973), 45, 247, (1975).

    Google Scholar 

  19. G. Jona-Lasinio, in “New Developments” (see ref. 8).

    Google Scholar 

  20. M.E. Fisher, Rev. Mod. Phys. 46, No4, 597, (1974).

    Google Scholar 

  21. D. Foerster, H.B. Nielsen, M. Ninomiya, Phys. Lett. 94 B, 135, (1980).

    Google Scholar 

  22. J. Iliopoulos, D.V. Nanopoulos and T.N. Tomaras, Phys. Lett. 94 B, 141, (1980).

    Google Scholar 

  23. Réf. 39 (Sect. 7); ref. 27; ref. 16.

    Google Scholar 

  24. K. Cahill and P. Denes, Preprint, Univ. New Mexico: UNMTP-81/020.

    Google Scholar 

  25. Refs. 39 and 27; J. Fröhlich and T. Spencer, Phase Diagrams and Critical Properties of Classical Coulomb Systems, Erice 1980.

    Google Scholar 

  26. C. Newman and L. Schulman,“Asymptotic Symmetry: Enhancement and Stability,” submitted to Phys. Rev. Letters.

    Google Scholar 

  27. L. Michel and L. Radicati, Ann. Phys. (NY) 66, 758, (1971).

    Google Scholar 

  28. D. Kastler et al., Commun. math. Phys. 27, 195, (1972).

    Google Scholar 

  29. J. Fröhlich, G. Morchio and F. Strocchi, Ann. Phys. (N.Y.) 119, 241, (1979), Phys. Lett. 89 B, 61, (1979).

    Google Scholar 

  30. Ph. Martin, Preprint, EPF-Lausanne, 1981.

    Google Scholar 

  31. N.D. Mermin, J. Math. Phys. 8, 1061, (1967).

    Google Scholar 

  32. J. Phys. Soc. Japan, Suppl. 26, 203, (1969).

    Google Scholar 

  33. S. Coleman, Commun. math. Phys. 31, 259, (1974). See also ref. 6.

    Google Scholar 

  34. J. Fröhlich and C. Pfister, Commun. math. Phys. (1981).

    Google Scholar 

  35. H. Kunz and C. Pfister, Commun. math. Phys. 46, 245, (1976).

    Google Scholar 

  36. J. Fröhlich, R. Israel, E.H. Lieb and B. Simon, Commun. math. Phys. 62, 1, (1978).

    Google Scholar 

  37. F. Dyson, E.H. Lieb and B. Simon, J. Stat. Phys. 18, 335, (1978).

    Google Scholar 

  38. E.H. Lieb, in “Mathematical Problems in Theoretical Physics”, G.F. Dell'Antonio, S. Doplicher and G. Jona-Lasinio (eds.), Springer Lecture Notes in Physics, BerlinHeidelberg-New York: Springer Verlag, 1978.

    Google Scholar 

  39. J. Fröhlich and T. Spencer, “Massless Phases and Symmetry Restoration....”, Commun. math. Phys., to appear.

    Google Scholar 

  40. A. Guth, Phys. Rev. D21, 2291, (1980).

    Google Scholar 

  41. S. Elitzur, R. Pearson and J. Shigemitsu, Phys. Rev. D19, 3698, (1979).

    Google Scholar 

  42. K. Wilson, Phys. Rev. D10, 2445, (1974).

    Google Scholar 

  43. K. Osterwalder and E. Seiler, Ann. Phys. (NY) 110, 440, (1978).

    Google Scholar 

  44. D. Brydges, J. Fröhlich and E. Seiler, Ann. Phys. (NY) 121, 227, (1979).

    Google Scholar 

  45. E. Seiler, “Gauge Theories as a Problem of Constructive Quantum Field Theory and Statistical Mechanics”, Springer Lecture Notes in Physics, to appear.

    Google Scholar 

  46. H. van Beijeren, Commun. math. Phys. 40, 1, (1975), Phys. Rev. Lett. 38, 993, (1977); ref. 39, (Sect. 7); C. Itzykson, M.E. Peskin and J.-B. Zuber, Phys. Lett. 95 B, 259, (1980); A. Hasenfratz, E. Hasenfratz and P. Hasenfratz, Nucl. Phys. B180, 353, (1981); M. L:uscher, DESY Preprint 1980.

    Google Scholar 

  47. G. Morchio and F. Strocchi, Phys. Lett. lQ4 B, 277, (1981).

    Google Scholar 

  48. J. Glimm, A. Jaffe and T. Spencer, Commun. math. Phys. 45, 203 (1975)

    Google Scholar 

  49. R. Dobrushin and S. Schlosman, Preprint 1981.

    Google Scholar 

  50. J. Fröhlich, “The Statistical Mechanics of Defect Gases”, unpublished.

    Google Scholar 

  51. D. Brydges and P. Federbush, Commun. math. Phys. 62, 79, (1978); D. Brydges, J. Fröhlich and T. Spencer, “The Random Walk Representation of Classical Spin Systems and Correlation Inequalities”, Commun. math. Phys., to appear.

    Google Scholar 

  52. J. Fröhlich and T. Spencer, “The Kosterlitz-Thouless Transition in Two-Dimensional Abelian Spin Systems and the Coulomb Gas”, Commun. math. Phys. to appear.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institut des Hautes Etudes Scientifiques, 35, route de Chartres, F-91440, Bures-sur-Yvette

    Jürg Fröhlich

Authors
  1. Jürg Fröhlich
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

P. Breitenlohner H. P. Dürr

Rights and permissions

Reprints and permissions

Copyright information

© 1982 Springer-Verlag

About this paper

Cite this paper

Fröhlich, J. (1982). Spontaneously broken and dynamically enhanced global and local symmetries. In: Breitenlohner, P., Dürr, H.P. (eds) Unified Theories of Elementary Particles. Lecture Notes in Physics, vol 160. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-11560-9_7

Download citation

  • DOI: https://doi.org/10.1007/3-540-11560-9_7

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-11560-1

  • Online ISBN: 978-3-540-39250-7

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation