Skip to main content

The Explicit Nonlinearity of Quantum Electrodynamics

  • Chapter
The Electron

Part of the book series: Fundamental Theories of Physics ((FTPH,volume 45))

Abstract

The underlying presumptions and principal features of major semiclassical theories of radiation are examined critically. There are significant physical and mathematical difficulties leading to the conclusion that, in their present state of development, these theories are incapable of competing with QED either qualitatively or quantitatively. Some possible means of salvaging the semiclassical approach are suggested, the motivation being to seek a more physically satisfying picture than that provided by quantum field theory.

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 129.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 169.99
Price excludes VAT (USA)
  • Durable hardcover 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

  • Babiker, M.: 1975, ’Source-Field Approach to Radiative Corrections and Semiclassical Radiation Theory’, Phys. Rev. A 12, 1911.

    Article  ADS  Google Scholar 

  • Barut, A.O.: 1988, ’Quantum-Electrodynamics Based on Self-Energy’, Physica Scripta T21, 18.

    Article  ADS  Google Scholar 

  • Barut, A.O., and J.P. Dowling: 1987, ‘Quantum Electrodynamics Based on Self-Energy, without Second Quantization: The Lamb Shift and Long-Range Casimir-Polder van der Waals Forces Near Boundaries’, Phys. Rev. A 36, 2550.

    Article  ADS  Google Scholar 

  • Barut, A.O., and J.P. Dowling: 1989, ‘QED Based on Self-Fields: A Relativistic Calculation of g - 2’, Z. f. Naturf. 44a, 105.

    Google Scholar 

  • Barut, A.O., and Y.I. Salamin: 1988, ‘Relativistic Theory of Spontaneous Emission’, Phys. Rev. A 37, 2284.

    Article  ADS  Google Scholar 

  • Barut, A.O., and N. Unal: 1990, ‘Regularized Analytic Evaluation of Vacuum Polarization in a Coulomb Field’, Phys. Rev. D 41, 3822.

    Article  MathSciNet  ADS  Google Scholar 

  • Barut, A.O., and J.F. Van Huele: 1985, ’Quantum Electrodynamics Based on Self-Energy: Lamb Shift and Spontaneous Emission without Field Quantization’, Phys. Rev. A 32, 3187.

    Article  ADS  Google Scholar 

  • Berestetskii, V.B., E.M. Lifshitz, and L.P. Pitaevskii: 1982, Quantum Electrodynamics, Pergamon Press, Oxford.

    Google Scholar 

  • Bethe, H.A.: 1947, ’The Electromagnetic Shift of Energy Levels’, Phys. Rev. 72, 339.

    Article  ADS  MATH  Google Scholar 

  • Bialynicki-Birula, I.: 1986, ’Comment on “Quantum Electrodynamics Based on Self-Energy: Lamb Shift and Spontaneous Emission without Field Quantization’, Phys. Rev. A 34, 3500.

    Article  ADS  Google Scholar 

  • Bjorken, J.D., and S.D. Drell: 1964, Relativistic Quantum Mechanics, McGraw-Hill, New York.

    Google Scholar 

  • Citron, M.L., H.R. Gray, C.W. Gabel, and C.R. Stroud: 1977, ‘Experimental Study of Power Broadening in a Two-Level Atom’, Phys. Rev. A 16, 1507.

    Article  ADS  Google Scholar 

  • Crisp, M.D., and E.T. Jaynes: 1969, ‘Radiative Effects in Semiclassical Theory’, Phys. Rev. 179, 1253.

    Article  ADS  Google Scholar 

  • Das, A., and D. Kay: 1989, ‘A Class of Exact Plane Wave Solutions of the Maxwell-Dirac Equations’, J. Math. Phys. 30, 2280.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  • Davies, B., and A.N. Burkitt: 1980, ‘On the Relationship between Quantum Random and Semiclassical Electrodynamics’, Aust. J. Phys.33 : 671.

    MathSciNet  ADS  Google Scholar 

  • Dorling, J.: 1987, ’Schrödinger’s Original Interpretation of the Schrödinger Equation: A Rescue Attempt’, in C.W. Kilmister (ed.), Schrödinger, Cambridge Univ. Press, Cambridge, p.16.

    Google Scholar 

  • Finkelstein, R.J.: 1949, ’On the Quantization of a Unified Field Theory’, Phys. Rev. 75, 1079.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  • Finkelstein, R., C. Fronsdal, and P. Kaus: 1956, ‘Nonlinear Spinor Field’, Phys. Rev. 103, 1571.

    Article  ADS  MATH  Google Scholar 

  • Flato, M., J. Simon, and E. Taflin: 1987, ‘On Global Solutions of the Maxwell-Dirac Equations’, Commun. Math. Phys. 112, 21.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  • French, J.B., and V.F. Weisskopf: 1949, The Electromagnetic Shift of Energy Levels’, Phys. Rev. 75, 1240.

    Article  ADS  MATH  Google Scholar 

  • Goldman, S.P., and G.W.F. Drake: 1981, ‘Relativistic Two-Photon Decay Rates of 2S1/2 Hydrogenic Ions’, Phys. Rev. A 24, 183.

    Article  ADS  Google Scholar 

  • Grandy, W.T., Jr.: 1991, Relativistic Quantum Mechanics of Leptons and Fields, Kluwer, Dordrecht.

    Book  Google Scholar 

  • Grandy, W.T., Jr., and A. Aghazadeh: 1982, ‘Radiative Corrections for Extended Charged Particles in Classical Electrodynamics’, Ann. Phys. 142, 284.

    Article  MathSciNet  ADS  Google Scholar 

  • Itzykson, C., and J.-B. Zuber: 1980, Quantum Field Theory, McGraw-Hill, New York.

    Google Scholar 

  • Jaynes, E.T.: 1973, ‘Survey of the Present Status of Neoclassical Radiation Theory’, in L. Mandel and E. Wolf (eds.), Coherence in Quantum Optics, Plenum, New York.

    Google Scholar 

  • Jaynes, E.T.: 1978, ‘Electrodynamics Today’, in L. Mandel and E. Wolf (eds.), Coherence in Quantum Optics IV, Plenum, New York.

    Google Scholar 

  • Jaynes, E.T.: 1990, ‘Probability in Quantum Theory’, in W.H. Zurek (ed.), Complexity, Entropy and the Physics of Information, Addison-Wesley, Reading, MA.

    Google Scholar 

  • Kaempffer, F.A.: 1955, ‘Elementary Particles as Self-Maintained Excitations’, Phys. Rev. 99, 1614.

    Article  ADS  Google Scholar 

  • Källén, A.O.G.: 1958, ‘Quantenelektrodynamik’, in S. Flügge (ed.), Handbuch der Physik, Band V, Teil 1, Springer-Verlag, Berlin.

    Google Scholar 

  • Khalatnikov, I.M.: 1989, ‘Reminiscences of Landau’, Physics Today, May, p.34.

    Google Scholar 

  • Kimble, H.J., and L. Mandel: 1975, ‘Problem of Resonance Fluorescence and the Inadequacy of Spontaneous Emission as a Test of Quantum Electrodynamics’, Phys. Rev. Lett. 34, 1485.

    Article  ADS  Google Scholar 

  • Lanyi, G.: 1973, 5Classical Electromagnetic Radiation of the Dirac Electron’, Phys. Rev. D 8, 3413.

    Article  ADS  Google Scholar 

  • Lloyd, S.P.: 1950, ‘Elimination of the Self-Electromagnetic Field’, Phys. Rev. 77, 757(A).

    MathSciNet  Google Scholar 

  • Mahanty, J.: 1974, ‘A Semi-Classical Theory of the Dispersion Energy of Atoms and Molecules’, Nuovo Cimento 22B, 110.

    ADS  Google Scholar 

  • Mandel, L.: 1986, ‘Non-Classical States of the Electromagnetic Field’, Phys. Scripta T12, 34.

    Article  ADS  Google Scholar 

  • Mathieu, P., and T.F. Morris: 1984, ‘Existence Conditions for Spinor Solitons’, Phys. Rev. D 30, 1835.

    Article  MathSciNet  ADS  Google Scholar 

  • Milonni, P.W.: 1984, ‘Why Spontaneous Emission?’, Am. J. Phys. 52, 340.

    Article  ADS  Google Scholar 

  • Power, E.A.: 1966, ‘Zero-Point Energy and the Lamb Shift’, Am. J. Phys. 34, 516.

    Article  ADS  Google Scholar 

  • Schwinger, J., L.L. DeRaad, Jr., and K.A. Milton: 1978, ’Casimir Effect in Dielectrics’, Ann. Phys. 115, 1.

    Article  MathSciNet  ADS  Google Scholar 

  • Schrödinger, E.: 1926, ‘Quantisierung als Eigenwertproblem’, Ann. d. Phys. 79, 361.

    Article  MATH  Google Scholar 

  • Schrödinger, E.: 1927, ‘Energieaustauch nach der Wellenmechanik’, Ann. d. Phys. 83, 956.

    Article  MATH  Google Scholar 

  • Stroud, C.R., Jr., and E.T. Jaynes: 1970, ‘Long-Term Solutions in Semiclassical Radiation Theory’, Phys. Rev. A 1, 106.

    Article  ADS  Google Scholar 

  • Uehling, E.A.: 1935, ‘Polarization Effects in the Positron Theory’, Phys. Rev. 48, 55.

    Article  ADS  MATH  Google Scholar 

  • Weisskopf, V., and E.P. Wigner: 1930, ‘Linienbreite auf Grund der Diracschen Lichttheorie’, Z. Phys. 63, 54.

    Article  ADS  MATH  Google Scholar 

  • Wódkiewicz, K.: 1980, ‘Resonance Fluorescence and Spontaneous Emission as Tests of QED’, in A.O. Barut (ed.), Foundations of Radiation Theory and Quantum Electrodynamics, Plenum, New York.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1991 Kluwer Academic Publishers

About this chapter

Cite this chapter

Grandy, W.T. (1991). The Explicit Nonlinearity of Quantum Electrodynamics. In: Hestenes, D., Weingartshofer, A. (eds) The Electron. Fundamental Theories of Physics, vol 45. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-3570-2_7

Download citation

  • DOI: https://doi.org/10.1007/978-94-011-3570-2_7

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-010-5582-6

  • Online ISBN: 978-94-011-3570-2

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics