Skip to main content

Should We Believe in Quantum Field Theory?

  • Chapter
The Whys of Subnuclear Physics

Part of the book series: The Subnuclear Series ((SUS,volume 15))

Abstract

The following is a straightforward attempt to answer the question stated in the title and posed by Professor Zichichi in his opening lecture of the School. Its perspective is to some extent historical as is appropriate, in my opinion, for part of an attempt to assess where we are and where we are going in the study of sub-nuclear matter. If there are readers who are not aware of the inherent fallibility of such attempts to learn from history, they should be reminded that the method involved is somewhat reminiscent of that used by the celebrated wise men of Chelm, who, when they wished to record the location of an especially good fishing spot, carefully marked the place on the boat from which they were fishing.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 74.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever

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. For a more detailed discussion see A.S. Wightman, Mathematical Idealization and Theoretical Physics; The Role of Mathematical Physics, Progress in Scientific Culture 1 (1976) 19.

    Google Scholar 

  2. M. Born, W. Heisenberg and P. Jordan, Zur Quantenmechanik II, Z. für Phys. 35 (1925) 606.

    Google Scholar 

  3. P.A.M. Dirac, The Quantum Theory of the Absorption and Emission of Radiation, Proc. Royal Soc. London A114 (1927) 243.

    ADS  Google Scholar 

  4. W. Heisenberg, Uber die in der Theorie der Elementarteilchen auftretende universelle Länge, Ann. der Physik (5) 32 (1938) 20.

    Article  Google Scholar 

  5. W. Heisenberg, Z. für Phys. 101 (1936) 533.

    Article  ADS  Google Scholar 

  6. W. Heisenberg, Die “beobachtbaren Grössen” in der Theorie der Elementarteilchen I, Z. für Phys. 120 (1943) 513.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  7. W. Heisenberg, Die “beobachtbaren Grössen” in der Theorie der Elementarteilchen I, Z. für Phys. II 120 (1943) 673.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  8. L. Van Hove, Sur l’operateur Hamiltonian de deux champs quantifiés en intéraction, Bulletin de l’Académie royale de Belgique 37 (1951) 1055.

    MATH  Google Scholar 

  9. B. Simon, Perturbation Theory and Coupling Constant Analyticity in Two-Dimensional Field Theories in “Fundamental Interactions in Physics and Astrophysics”, p. 120, Eds. G. Iverson, A. Perlmutter and S. Mintz, Plenum Press (1973).

    Google Scholar 

  10. F.J. Dyson, Divergence of Perturbation in Quantum Electrodynamics, Phys. Rev. 85 (1952) 631.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  11. For a general review, see the proceedings of the 1973 Erice Mathematical Physics School, Constructive Quantum Field Theory, Eds. G. Velo and A. Wightman, Lecture Notes in Physics No. 25, Springer-Verlag, Berlin (1973).

    Google Scholar 

  12. J. Eckmann, J. Magnen and R. Sénéor, Decay Properties and Borel Summability for the Schwinger Functions in P(Φ)2 Theories, Commun. Math. Phys. 39 (1975) 251.

    Article  ADS  Google Scholar 

  13. J, Eckmann, H. Epstein and J. Fröhlich, Asymptotic Perturbation Expansion for the S-Matrix and the Definition of Time-Ordered Functions in Relativistic Quantum Field Theory Models, Ann. Inst. Henri Poincaré XXV (1976) 1.

    Google Scholar 

  14. N.N. Khuri, Solutions of the Callan-Symanzik Equation in a Complex Neighbourhood of Zero Coupling, Phys. Rev. D12 (1975) 2298.

    MathSciNet  ADS  Google Scholar 

  15. J. Glimm, A. Jaffe and T. Spencer, A Convergent Expansion about Mean Field Theory, I II Ann. of Physics 101. (1976) 610 and 631.

    MathSciNet  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1979 Plenum Press, New York

About this chapter

Cite this chapter

Wightman, A.S. (1979). Should We Believe in Quantum Field Theory?. In: Zichichi, A. (eds) The Whys of Subnuclear Physics. The Subnuclear Series, vol 15. Springer, Boston, MA. https://doi.org/10.1007/978-1-4684-0991-8_18

Download citation

  • DOI: https://doi.org/10.1007/978-1-4684-0991-8_18

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4684-0993-2

  • Online ISBN: 978-1-4684-0991-8

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics