Skip to main content
SpringerLink
Log in

The Quantum Noether Condition in Terms of Interacting Fields

  • Conference paper
  • First Online:
Quantum Field Theory

Part of the book series: Lecture Notes in Physics ((LNP,volume 558))

Abstract

We review our recent work, hep-th/9803030, on the constraints imposed by global or local symmetries on perturbative quantum field theories. The analysis is performed in the Bogoliubov-Shirkov-Epstein-Glaser formulation of perturbative quantum field theory. In this formulation the S-matrix is constructed directly in the asymptotic Fock space with only input causality and Poincare invariance. We reformulate the symmetry condition proposed in our earlier work in terms of interacting Noether currents.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. N. Seiberg and E. Witten, Monopole Condensation, And Confinement In N = 2 Supersymmetric Yang-Mills Theory, Nucl.Phys. B426 (1994) 19, hep-th/9407087; N. Seiberg, Electric-Magnetic Duality in Supersymmetric Non-Abelian Gauge The ories, Nucl.Phys. B435 (1995) 129, hep-th/9411149.

    Article  ADS  MathSciNet  Google Scholar 

  2. T. Hurth and K. Skenderis, Quantum Noether Method, Nucl. Phys. B541(1999) 566–614, hep-th/9803030.

    Article  ADS  MathSciNet  Google Scholar 

  3. C. Becchi, A. Rouet, and R. Stora, Renormalization of the Abelian Higgs-Kibble Model, Comm. Math. Phys. 42 (1975) 127; Renormalizable Models with Broken Symmetries, in Renormalization Theory, ed. by G. Velo and A.S. Wightman (Reidel, Dordrecht, 1976); Ann. Phys. 98 (1976) 287; I.V. Tyutin, Lebenev Institute preprint N39 (1975).

    Article  ADS  MathSciNet  Google Scholar 

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

    Google Scholar 

  5. H. Epstein and V. Glaser, in: Statistical Mechanics and Quantum Field Theory, Proceedings of the 1970 Summer School of Les Houches, eds. C. de Witt and R. Stora, New York, Gordon and Breach, 1971; H. Epstein and V. Glaser, The Role of Locality in Perturbation Theory, Ann. Inst. Poincaré 29 (1973) 211; H. Epstein and V. Glaser, Adiabatic Limit in Perturbation Theory, in G. Velo, A.S. Wightman (eds.), Renomnalization Theory, D. Reidel Publishing Company, Dordrecht 1976, 193; O. Piguet and A. Rouet,Symmetries in Perturbative Quantum Field theory, Phys. Rep. 76 (1981) 1.

    Google Scholar 

  6. H. Epstein, V. Glaser and R. Stora, General Properties of the n-Point Functions in Local Quantum Field Theory, in J. Bros, D. Jagolnitzer (eds.), Les Houches Proceedings 1975; G. Popineau and R. Stora, A Pedagogical Remark on the Main Theorem of Perturbative Renormalization Theory, unpublished; R. Stora, Differential Algebras, ETH-lectures (1993) unpublished.

    Google Scholar 

  7. R. Brunetti and K. Fredenhagen, Interacting Quantum Fields in Curved Space: Renormalizability of Ï•4, hep-th/9701048.

    Google Scholar 

  8. S. Deser, Self-interaction and Gauge Invariance, Gen. Rel. and Grav. I, 1 (1970) 9.

    Article  ADS  MathSciNet  Google Scholar 

  9. D.Z. Freedman, P. van Nieuwenhuizen and S. Ferrara, Progress towards a Theory of Supergravity, Phys. Rev. D14 (1976) 912; S. Deser and B. Zumino, Consistent Supergravity, Phys. Lett.B62 (1976) 335; S. Ferrara, F. Gliozzi, J. Scherk and P. van Nieuwenhuizen, Matter Couplings in Supergravity Theory, Nucl. Phys. B117 (1976) 333; P. van Nieuwenhuizen, Supergravity, Phys. Rep. 68 (1981) 191.

    ADS  Google Scholar 

  10. T. Kugo and I. Ojima, Local covariant operator formalism of non-abelian gauge theories and quark confinement problem, Suppl. Progr. Theor. Phys. 66 (1979) 1.

    Article  ADS  Google Scholar 

  11. M. Dütsch and K. Fredenhagen, A local (perturbative) construction of observables in gauge theories: the example of QED, hep-th/9807078; Deformation stability of BRST-quantization, hep-th/9807215.

    Google Scholar 

  12. J. Wess and B. Zumino, Consequences of Anomalous Ward Identities, Phys. Lett. B37 (1971) 95.

    ADS  MathSciNet  Google Scholar 

  13. T. Hurth and K. Skenderis, Analysis of Anomalies in the Quantum Noether Method, in preparation.

    Google Scholar 

  14. G. Barnich, M. Henneaux, T. Hurth and K. Skenderis, Cohomological analysis of gauged-fixed gauge theories, hep-th/9910201.

    Google Scholar 

  15. I. A. Batalin and G. A. Vilkovisky, Gauge algebra and quantization, Phys. Lett. B102; Quantization of Gauge Theories with Linearly Dependent Generators, (1981) 27, Phys. Rev. D28 (1983) 2567.

    Google Scholar 

  16. M. Henneaux and C. Teitelboim, Quantization of Gauge Systems, Princeton University Press, Princeton, 1992; J. Gomis, J. Paris and S. Samuel, Antibracket, Antifields and Gauge-Theory Quantization, Phys. Rep. 259 (1995) 1.

    MATH  Google Scholar 

  17. G. Scharf, Finite Quantum Electrodynamics, The Causal Approach, Text and Monographs in Physics, Springer, Berlin 1995.

    Google Scholar 

  18. T. Hurth, Nonabelian Gauge Theories: The Causal Approach, Annals of Phys. 244 (1995) 340, hep-th/9411080.

    Article  MATH  ADS  MathSciNet  Google Scholar 

  19. B. Malgrange, Seminaire Schwartz 21 (1960).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Max-Planck-Institute for Physics, Werner-Heisenberg-Institute, Fohringer Ring 6, D-80805, Munich, Germany

    Tobias Hurth

  2. Spinoza Institute, University of Utrecht, Leuvenlaan 4, 3584, CE Utrecht, The Netherlands

    Kostas Skenderis

Authors
  1. Tobias Hurth
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Kostas Skenderis
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Max-Planck-Institut für Physik, Werner-Heisenberg-Institut, Föhringer Ring 6, 80805, München, Germany

    Peter Breitenlohner  & Dieter Maison  & 

Rights and permissions

Reprints and permissions

Copyright information

© 2000 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Hurth, T., Skenderis, K. (2000). The Quantum Noether Condition in Terms of Interacting Fields. In: Breitenlohner, P., Maison, D. (eds) Quantum Field Theory. Lecture Notes in Physics, vol 558. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44482-3_6

Download citation

  • DOI: https://doi.org/10.1007/3-540-44482-3_6

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-67972-1

  • Online ISBN: 978-3-540-44482-4

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation