Skip to main content
SpringerLink
Log in
Book cover

Mathematical Problems in Theoretical Physics pp 319–323Cite as

Conformal invariance IN (gauge) quantum field theory

  • Group theory
  • Conference paper
  • First Online:

Part of the book series: Lecture Notes in Physics ((LNP,volume 153))

Abstract

The talk is meant as a brief up-to-date review of conformal Quantum Field Theory (QFT) including a preliminary report on a work in progress on conformal invariance in Quantum Electrodynamics (QED).

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. G. Mack, Abdus Salam: Finite component field representations of the conformal group. Ann. Phys. (N.Y.) 53, 174 (1969)

    Google Scholar 

  2. M. Plato, J. Simon, D. Sternheimer: Conformal covariance of field equations. Ann. Phys. (N.Y.) 61, 78 (1970)

    Google Scholar 

  3. D.J. Gross, J. Wess: Scale invariance and the high energy behaviour of scattering amplitude. Phys. Rev. D 2, 753 (1970)

    Google Scholar 

  4. A.M. Polyakov: Conformal symmetry of crucial fluctuations. Zh. Eksp. Teor, Piz., Pis. Red. 12, 538 (1970) (Engl. transl. JETP Lett. 12, 381 (1970))

    Google Scholar 

  5. A.A. Migdal: Conformal invariance and bootstrap. Phys. Letters 37 B, 386 (1971)

    Google Scholar 

  6. G. Parisi, L. Peliti: Calculation of critical indices, Lett. Nuovo, Cim. 2, 627 (1971)

    Google Scholar 

  7. G. Mack, I.T. Todorov: Conformal invariant Green functions without ultraviolet divergences. Phys. Rev. D 8, 1764 (1973)

    Google Scholar 

  8. G. Mack: Group theoretical approach in conformal invariant Quantum Field Theory, in Renormalization and Invariance in Quantum Field Theory, ed. by Caianiello (Plenum Press, N.Y. 1974) pp. 123–157; see also S. Ferrara, R. Gatto, A. Grillo, G. Parisi: General consequences of conformal algebra (as well as earlier work of Ferrara et al. cited there) and G. Mack: Conformal invariant Quantum Field Theory, in: Scale and Conformal Symmetry in Hadron Physics, ed. R. Gatto (Wiley, N. Y. 1973) pp. 59–108 and 109–130

    Google Scholar 

  9. A. M. Polyakov: Nonhamiltonian approach in the conformal invariant Quantum Field Theory. Zh. Eksp.Teor. Fiz. 66, 23 (1974) (Engl. transl. JETP 39, 10 (1974))

    Google Scholar 

  10. V.K. Dobrev, V.B. Petkova, S.G. Petrova, I.T. Todorov: Dynamical derivation of vacuum operator product expansion in Euclidean conformal Quantum Field Theory. Phys. Rev. D 13, 887 (1976)

    Google Scholar 

  11. V.K. Dobrev, G. Mack, V.B. Petkova, S.G. Petrova, I.T. Todorov: Harmonic Analysis on the n-Dimensional Lorentz Group and its Application to Conformal Quantum Field Theory Lecture Notes in Physics, 63, (Springer-Verlag, Berlin 1977)

    Google Scholar 

  12. I.T. Todorov, M.C. Mintchev, V.B. Petkova: Conformal Invariance in Quantum Field Theory. (Scuola Normale Superiore, Pisa 1978)

    Google Scholar 

  13. E.S. Fradkin, M. Ya. Palchik: Recent developments in conformal invariant QFT. Phys. Reports 44 C, 249 (1978)

    Google Scholar 

  14. E.S. Fradkin, M. Ya. Palchik, V.N. Zaikin: Calculation on anomalous dimensions in conformally invariant Field Theory. J. Phys. A. Math. Gen. 13, 3429 (1980)

    Google Scholar 

  15. M.Ya. Palchik: Problems of dynamics in conformal invariant Field Theory. Proceedings of the IIId School on Elementary Particles and High Energy Physics in Primorsko, Bulgaria 1977 (Sofia 1978) pp. 240–258

    Google Scholar 

  16. M.Ya. Palchik: On the operator product jμ (x) ϕ (x) in the Thirring model. Short Commun. in Physics, No. 4 (Lebedev Phys. Institute, Moscow 1980) (in Russian)

    Google Scholar 

  17. M. Mintchev, V. Petkova, I. Todorov: Scale and conformal covariance in Quantum Electrodynamics. Rep. Math. Phys. 9, 355 (1976) (For a slightly revised and extended version see chapter VII of ref. [12].)

    Google Scholar 

  18. D. Zwanziger: Lesson of a soluble model of Quantum Electrodynamics. Phys. Rev. D 17, 457 (1978)

    Google Scholar 

  19. V.K. Dobrev, V.B. Petkova: Elementary representations and intertwining operators for SU*(4) Rep. Math. Phys. 13, 233 (1978)

    Google Scholar 

  20. G. Mack: All unitary ray representations of the conformal group SU(2,2) with positive energy. Commun. Math. Phys. 55 1 (1977)

    Google Scholar 

Download references

Author information

Author notes

  1. I.T. Todorov

    Present address: Institute of Nuclear Research and Nuclear Energy, Bulgarian Academy of Sciences, 1184, Sofia, Bulgaria

Authors and Affiliations

  1. Fakultät für Physik, Universität Bielefeld, 4800, Bielefeld 1

    I.T. Todorov

Authors
  1. I.T. Todorov
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

R. Schrader R. Seiler D. A. Uhlenbrock

Rights and permissions

Reprints and permissions

Copyright information

© 1982 Springer-Verlag

About this paper

Cite this paper

Todorov, I. (1982). Conformal invariance IN (gauge) quantum field theory. In: Schrader, R., Seiler, R., Uhlenbrock, D.A. (eds) Mathematical Problems in Theoretical Physics. Lecture Notes in Physics, vol 153. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-11192-1_57

Download citation

  • DOI: https://doi.org/10.1007/3-540-11192-1_57

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-11192-4

  • Online ISBN: 978-3-540-38982-8

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation