Abstract
Some reflection on the preceding chapters indicates that the Dirac equation, even modified to include external fields, is not yet complete. One of the major lessons of classical electrodynamics is that accelerated charged particles radiate (though this is not necessarily true for all charge distributions), and energy conservation alone requires the dynamical equations of motion to account for this phenomenon. Although we have paid lip service to such a requirement in Eqs.(3–110)-(3–113), a detailed study can be postponed no longer.
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References
Ackerhalt, J.R., P.L. Knight, and J.H. Eberly: 1973, ‘Radiation Reaction and Radiative Frequency Shifts’, Phys. Rev. Lett. 30, 456.
Aitchison, I.J.R.: 1985, ‘Nothing’s Plenty’, Contemp. Phys. 26, 333.
Allen, L., and J.H. Eberly: 1975, Optical Resonance and Two-Level Atoms, Wiley, New York.
Andrews, D.A., and G. Newton: 1976, ‘Radio Frequency Atomic Beam Measurement of the \( \left( {{2^2}{S_{{\frac{1}{2}}}}, \,F = 0} \right) - \left( {{2^2}{P_{{\frac{1}{2}}}}\,F = 1} \right) \) Lamb-Shift Interval’, Phys. Rev. Lett. 37, 1254.
Bailey, J., K. Borer, F. Combley, H. Drumm, F.J.M. Farley, J.H. Field, W. Flegel, P.M. Hattersley, F. Krienen, F. Lange, E. Picasso, and W. Von Rüden: 1977, ‘The Anomalous Magnetic Moment of Positive and Negative Muons’, Phys. Lett. 68B, 191.
Barton, G.: 1974, ‘Frequency Shifts Near an Interface: Inadequacy of Two-Level Atomic Models’, J. Phys. B 7, 2134.
Barut, A.O.: 1968, ‘Reformulation of the Dirac Theory of the Electron’, Phys. Rev. Lett. 20, 893.
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.
Barut, A.O., and Y.I. Salamin: 1988, ‘Relativistic Theory of Spontaneous Emission’, Phys. Rev. A 37, 2284.
Bell, J.S.: 1987, Speakable and Unspeakable in Quantum Mechanics, Cambridge Univ. Press, Cambridge.
Bethe, H.A.: 1947, ‘The Electromagnetic Shift of Energy Levels’, Phys. Rev. 72, 339.
Bethe, H.A., and E.E. Salpeter: 1977, Quantum Mechanics of One- and Two-Electron Atoms, Plenum Press, New York.
Berestetskii, V.B., E.M. Lifshitz, and L.P Pitaevskii: 1982, Quantum Electrodynamics, Pergamon Press, Oxford.
Bjorken, J.D., and S.D. Drell: 1964, Relativistic Quantum Mechanics, McGraw-Hill, New York.
Bjorken, J.D., and S.D. Drell: 1965, Relativistic Quantum Fields, McGraw-Hill, New York.
Bloch, F.: 1946, ‘Nuclear Induction’, Phys. Rev. 70, 460.
Bloch, F., and A. Nordsieck: 1937, ‘Note on the Radiation Field of the Electron’, Phys. Rev. 52, 54.
Bohr, N., and L. Rosenfeld: 1933, ‘Für Frage der Messbarkeit der elektromagnetischen Feldgrössen’, Kgl. Danske Videnskab. Selskab, Mat.-Fys. Medd. 12, 1.
Born, M., W. Heisenberg, and P. Jordan: 1926, ‘Zur Quantenmechanik. II’, Z. Phys. 35, 557.
Breit, G.: 1947, ‘Does the Electron Have an Intrinsic Magnetic Moment?’, Phys. Rev. 72, 984.
Brodsky, S.J., and S.D. Drell: 1980, ‘Anomalous Magnetic Moment and Limits on Fermion Substructure’, Phys. Rev. D 22, 2236.
Brown, L.M., and L. Hoddeson (eds.): 1983, The Birth of Particle Physics, Cambridge Univ. Press, Cambridge.
Calmet, J., S. Narison, M. Perrottet, and E. de Rafael: 1977, ‘The Anomalous Magnetic Moment of the Muon: A Review of the Theoretical Contributions’, Rev. Mod. Phys. 49, 21.
Casimir, H.B.G.: 1948, ‘On the Attraction between Two Perfectly Conducting Plates’, Proc. K. Nedd. Acad. Weten. 51, 793.
Casimir, H.B.G., and D. Polder: 1948, ‘The Influence of Retardation on the London-van der Waals Forces’, Phys. Rev. 73, 360.
Chadam, J.M.: 1972, ‘On the Cauchy Problem for the Coupled Maxwell-Dirac Equations’, J. Math. Phys. 13, 597.
Chow, W.W., M.O. Scully, and J.O. Stoner, Jr.: 1975, ‘Quantum Beat Phenomena Described By Quantum Electrodynamics and Neoclassical Theory’, Phys. Rev. A 11, 1380.
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.
Crisp, M.D., and E.T. Jaynes: 1969, ‘Radiative Effects in Semiclassical Theory’, Phys. Rev. 179, 1253.
Dalibard, J., J.Dupont-Roc, and C. Cohen-Tannoudji: 1982, ‘Vacuum Fluctuations and Radiation Reaction: Identification of their Respective Contributions’, J. Physique 43, 1617.
Das, A., and D. Kay: 1989, ‘A Class of Exact Plane Wave Solutions of the Maxwell-Dirac Equations’, J. Math. Phys. 30, 2280.
Davies, B., and A.N. Burkitt: 1980, ‘On the Relationship between Quantum, Random and Semiclassical Electrodynamics’, Aust. J. Phys. 33, 671.
Delbrück, M.: 1933, ‘Zusatz zu der Arbeit L. Meitner und H. Kösters, “Über die Streung kurzwelliger γ-Strahlen’, Z. Phys. 84, 144.
Dicke, R.H.: 1954, ‘Coherence in Spontaneous Radiation Processes’, Phys. Rev. 93, 99.
Dirac, P.A.M.: 1927, ‘The Quantum Theory of the Emission and Absorption of Radiation’, Proc. Roy. Soc. (London) A114, 243.
Dirac, P.A.M.: 1977, ‘The Relativistic Electron Wave Equation’, Europhys. News, October 1977, p.1. [Lecture Delivered at the European Conference on Particle Physics, Budapest, 4 July 1977.]
Dodd, J.N.: 1983, ‘The Compton Effect—A Classical Treatment’, Eur. J. Phys. 4, 205.
Dorling, J.: 1987, ‘Schrödinger’s Original Interpretation of the Schrödinger Equation: A Rescue Attempt’, in C.W. Kilmister (ed.), Schrödinger, Cambridge Univ. Press, Cambridge.
Dyson, F.J.: 1952, ‘Divergence of Perturbation Theory in Quantum Electrodynamics’, Phys. Rev. 85, 631.
Dyson, F.: 1965, ‘Tomonaga, Schwinger, and Feynman’, Science 150, 588.
Einstein, A.: 1917, ‘Quantentheorie der Strahlung’, Phys. Z. 18, 121.
Erickson, G.W., and H. Grotch: 1988, ‘Lamb-Shift Recoil Effects in Hydrogen, Phys. Rev. Lett. 60, 2611. [Errata: Phys. Rev. Lett. 63, 1326(1989).]
Fain, B.: 1982, ‘Spontaneous Emission vs. Vacuum Fluctuations’, Nuovo Cimento B68, 73.
Fain, V.M., and Ya.I. Khanin: 1969, Quantum Electronics, Vol.1, M.I.T. Press, Cambridge, MA., p.211.
Fermi, E.: 1932, ‘Quantum Theory of radiation’, Rev. Mod. Phys. 4, 87.
Fermi, E.: 1934, ‘Versuch einer Theorie der β-Strahlen.I’, Z. Phys. 88, 161.
Feynman, R.P.: 1985, QED, Princeton Univ. Press, Princeton.
Finkelstein, R.J.: 1949, ‘On the Quantization of a Unified Field Theory’, Phys. Rev. 75, 1079.
Finkelstein, R.J., C. Fronsdal, and P. Kaus: 1956, ‘Nonlinear Spinor Field Theory’, Phys. Rev. 103, 1571.
French, J.B., and V.F. Weisskopf: 1949, ‘The Electromagnetic Shift of Energy Levels’, Phys. Rev. 75, 1240.
Frenkel, J.: 1926, ‘Die Elektrodynamik des rotierenden Elektrons’, Z. Phys. 37, 243.
Grammer, G., Jr., and D.R. Yennie: 1973, ‘Improved Treatment for the Infrared-Divergence Problem in Quantum Electrodynamics’, Phys. Rev. D 8, 4332.
Grandy, W.T., Jr.: 1970, Introduction to Electrodynamics and Radiation, Academic Press, New York, p.114.
Grandy, W.T., Jr.: 1991, ‘The Explicit Nonlinearity of Quantum Electrodynamics’, in A. Weingartshofer (ed.), The Electron-1990, Kluwer, Dordrecht.
Gross, L.: 1966, ‘The Cauchy Problem for the Coupled Maxwell and Dirac Equations’, Comm. Pure Appl. Math 19, 1.
Heber, O., B.B. Bandong, G. Sampoll, and R.L. Watson: 1990, ‘Observation of Quantum Beats in the Resonance Flourescence of Free Excitons’, Phys. Rev. Lett. 64, 854.
Heisenberg, W., and W. Pauli: 1929, ‘Zur Quantentheorie der Wellenfelder’, Z. Phys. 56, 1.
Heisenberg, W., and W. Pauli: 1930, ‘Zur Quantentheorie der Wellenfelder.II’, Z. Phys. 59, 168.
Hilgevoord, J., and E.A. DeKerf: 1965, ‘The Covariant Definition of Spin in Relativistic Quantum Field Theory’, Physica 31, 1002.
Hilgevoord, J., and S.A. Wouthuysen: 1963, ‘On the Spin Angular Momentum of the Dirac Particle’, Nucl. Phys. 40, 1.
Hocker, G.B., and C.L. Tang: 1968, ‘Observation of the Optical Transient Nutation Effect’, Phys. Rev. Lett. 21, 591.
Houston, W.V.: 1937, ‘A New Method of Analysis of the Structure of H α and D α ’, Phys. Rev. 51, 446.
Itzykson, C., and J.B. Zuber: 1980, Quantum Field Theory, McGraw-Hill, New York.
Jauch, J.M., and F. Rohrlich: 1955, The Theory of Photons and Electrons, Addison-Wesley, Reading, MA.
Jaynes, E.T.: 1973, ‘Survey of the Present Status of Neoclassical Radiation Theory’, in L. Mandel and E. Wolf (eds.), Coherence and Quantum Optics, Plenum Press, New York.
Jaynes, E.T.: 1978, ‘Electrodynamics Today’, in L. Mandel and E. Wolf (eds.), Coherence and Quantum Optics IV, Plenum Press, New York.
Jaynes, E.T.: 1980, ‘Quantum Beats’, in A.O. Barut (ed.), Foundations of Radiation Theory and Quantum Electrodynamics, Plenum Press, New York.
Jaynes, E.T.: 1990, ‘Probability in Quantum Theory’, in W.H. Zurek (ed.), Complexity, Entropy, and the Physics of Information, Addison-Wesley, Reading, MA.
Jaynes, E.T., and F.W. Cummings: 1963, ‘Comparison of Quantum and Semiclassical Radiation Theories with Application to the Beam Maser’, Proc. IEEE 51, 89.
Jordan, P.: 1928, ‘Der Charakter der Quantenphysik’, Naturwiss. 41, 765.
Jordan, P., and E. Wigner: 1928, ‘Über das Paulische Äquivalenzverbot’, Z. Phys. 47, 631.
Kaempffer, F.A.: 1955, ‘Elementary Particles as Self-Maintained Excitations’, Phys. Rev. 99, 1614.
Karplus, R., and N.M. Kroll: 1950, ‘Fourth Order Corrections in Quantum Electrodynamics and the Magnetic Moment of the Electron’, Phys. Rev. 77, 536.
Kim, Y.S., and M.E. Noz: 1986, Theory and Applications of the Poincaré Group, Reidel, Dordrecht.
Kimble, H.J., and L. Mandel: 1975, ‘Problem of Resonance Flourescence and the Inadequacy of Spontaneous Emission as a Test of Quantum Electrodynamics’, Phys. Rev. Lett. 34, 1485.
Kinoshita, T.: 1989, ‘Electron g — 2 and High Precision Determination of α’, in G.F. Bassani, M. Inguscio, and T.W. Hänsen (eds.), The Hydrogen Atom, Springer-Verlag, Berlin.
Kinoshita, T., and W.B. Lindquist: 1983a, ‘Eighth-Order Magnetic Moment of the Electron.I. Second-Order Vertex Containing Second-, Fourth-, and Sixth-Order Vacuum Polarization Subdiagrams’, Phys. Rev. D 27, 867.
Kinoshita, T., and W.B. Lindquist: 1983b, ‘Eighth-Order Magnetic Moment of the Electron.II. Fourth-Order Vertices Containing Second- and Fourth-Order Vacuum Polarization Subdiagrams’, Phys. Rev. D 27, 877.
Kinoshita, T., and W.B. Lindquist: 1983c, ‘Eighth-Order Magnetic Moment of the Elec-tron.III. Sixth-Order Vertices Containing a Second-Order Vacuum Polarization Sub-diagram’, Phys. Rev. D 27, 886.
Klein, O.: 1927, ‘Elektrodynamik und Wellenmechanik vom Standpunkt des Korrespodenzprinzips’, Z. Phys. 41, 407.
Klein, O., and Y. Nishina: 1929, ‘Über die Streung von Strahlung durch freie Elektronen nach der neuen relativistischen Quantendynamik von Dirac’, Z. Phys. 52, 853.
Kramers, H.A.: 1938, ‘Die Wechselwirkung zwischen geladenen Teilschen und Strahlungsfeld’, Z. Phys. 63, 54.
Kramers, H.A., and W. Heisenberg: 1925, ‘Über die Streung von Strahlung durch Atome’, Z. Phys. 31, 681.
Kurnit, N.A., I.D. Abella, and S.R. Hartmann: 1964, ‘Observation of a Photon Echo’, Phys. Rev. Lett. 13, 567.
Kusch, P., and H.M. Foley: 1947, ‘Precision Measurement of the ‘g Values’ in the 2 P 3/2 and 2 P 1/2 States of Gallium’, Phys. Rev. 72, 1256.
Lamb, G.L., Jr.: 1971, ‘Analytical Descriptions of Ultrashort Optical Pulse Propagation in a Resonant Medium’, Rev. Mod. Phys. 43, 99.
Lamb, W.E., Jr.: 1964, ‘Theory of an Optical Maser’, Phys. Rev. 134, A1429.
Lamb, W.E., Jr., and R.C. Retherford: 1947, ‘Fine Structure of the Hydrogen Atom by a Microwave Method’, Phys. Rev. 72, 241.
Lamb, W.E., Jr., and M.O. Scully: 1969, ‘The Photoelectric Effect without Photons’, in Société Francaise de Physique (ed.), Polarisation, matiere et rayonnement, Presses Univ. de France, Paris.
Lanyi, G.: 1973, ‘Classical Electromagnetic Radiation of the Dirac Electron’, Phys. Rev. D 8, 3413.
Lautrup, B.E., A. Peterman, and E. de Rafael: 1972, ‘Recent Developments in the Comparison between Theory and Experiments in Quantum Electrodynamics’, Phys. Repts. 3, 193.
Levine, M.J., and R. Roskies: 1976, ‘Analytic Contribution to the g Factor of the Electron in Sixth Order’, Phys. Rev. D. 14, 2191.
Lewis, G.N.: 1926, ‘The Conservation of Photons’, Nature 118, 874.
Lloyd, S.P.: 1950, ‘Elimination of the Self-Electromagnetic Field’, Phys. Rev. 77, 757(A).
London, F.: 1926, ‘Zur Theorie und Systematik den Molekularkräfte’, Z. Phys. 63, 245.
Loudon, R., and P.L. Knight: 1987, ‘Squeezed Light’, J. Mod. Opt. 34, 709.
Lundeen, S.R., and F.M. Pipkin: 1981, ‘Measurement of the Lamb Shift in Hydrogen, n = 2’, Phys. Rev. Lett. 46, 232.
Luttinger, J.M.: 1948, ‘A Note on the Magnetic Moment of the Electron’, Phys. Rev. 74, 893.
Mahanty, J.: 1974, ‘A Semi-Classical Theory of Dispersion Energy of Atoms and Molecules’, Nuovo Cimento 22B, 110.
McCall, S.L., and E.L. Hahn: 1967, ‘Self-Induced Transparency by Pulsed Coherent Light’, Phys. Rev. Lett. 18, 908.
Milonni, P.W.: 1976, ‘Semiclassical and Quantum-Electrodynamical Approaches in Non-relativistic Radiation Theory’, Phys. Repts. 25, 1.
Milonni, P.W.: 1984, ‘Why Spontaneous Emission?’, Am. J. Phys. 52, 340.
Milonni, P.W., J.R. Ackerhalt, and W.A. Smith: 1973, ‘Interpretation of Radiative Corrections in Spontaneous Emission’, Phys. Rev. Lett. 31, 958.
Nafe, J.E., E.B. Nelson, and I.I. Rabi: 1947, ‘The Hyperfine Structure of Atomic Hydrogen and Deuterium’, Phys. Rev. 71, 914.
Nagel, D.E., R.S. Julian, and J.R Zacharias: 1947, ‘Hyperfine Structure of Atomic Hydrogen and Deuterium’, Phys. Rev. 72, 971.
Pal’chikov, G., Yu.L. Sokolov, and V.P. Yakovlev: 1983, ‘Lifetime of the 2P State and Lamb Shift in the Hydrogen Atom’, JETP Lett 38, 418.
Pasternak, S.: 1938, ‘Note on the Fine Structure of H α and D α ’, Phys. Rev. 54, 1113.
Power, E.A.: 1964, Introductory Quantum Electrodynamics, American Elsevier, New York.
Power, E.A.: 1966, ‘Zero-Point Energy and the Lamb Shift’, Am. J. Phys. 34, 516.
Scharf, G.: 1989, Finite Quantum Electrodynamics, Springer-verlag, Berlin.
Schiff, L.I.: 1955, Quantum Mechanics, 2nd ed., McGraw-Hill, New York.
Schrödinger, E.: 1926, ‘Quantisierung als Eigenwertproblem’, Ann. d. Phys. 79, 361.
Schrödinger, E.: 1927, ‘Energieaustauch nach der Wellenmechanik’, Ann. d. Phys. 83, 956.
Schwarz, C.L., and J.J. Tiemann: 1959, ‘New Calculation of the Numerical Value of the Lamb Shift’, Ann. Phys. (N.Y.) 6, 178.
Schweber, S.S.: 1961, An Introduction to Relativistic Quantum Field Theory, Row, Peterson, Evanston, IL.
Schwinger, J.: 1948, ‘On Quantum-ELectrodynamics and the Magnetic Moment of the Electron’, Phys. Rev. 73, 416.
Schwinger, J. (ed.): 1958, Quantum Electrodynamics, Dover, New York.
Schwinger, J., L.L. De Raad, Jr., and K.A. Milton: 1978, ‘Casimir Effect in Dielectrics’, Ann. Phys. (N.Y.) 115, 1..
Senitsky, I.R.: 1973, ‘Radiation-Reaction and Vacuum-Field Effects in Heisenberg-Picture Quantum Electrodynamics’, Phys. Rev. Lett. 31, 955.
Senitsky, I.R.: 1978, ‘The Quantum Mechanical Foundations of Semiclassical Radiation Theories’, in L. Mandel and E. Wolf (eds.), Coherence and Quantum Optics IV, Plenum Press, New York.
Serber, R.: 1935, ‘Linear Modifications in the Maxwell Field Equations’, Phys. Rev. 48, 49.
Sommerfleld, C.M.: 1957, ‘Magnetic Dipole Moment of the Electron’, Phys. Rev. 107, 328.
Stroud, C.R., Jr., and E.T. Jaynes: 1970, ‘Long-Term Solutions in Semiclassical Radiation Theory’, Phys. Rev. A 1, 106.
Synge, J.L.: 1954, ‘On the Transfer of Energy between Electromagnetic Bodies’, Proc. Roy. Irish Acad. 56, 1.
Teller, P.: 1988, ‘Three Problems of Renormalization’, in H.R. Brown and R. Harré (eds.), Philosophical Foundations of Quantum Field Theory, Clarendon Press, Oxford.
Uehling, E.A.: 1935, ‘Polarization Effects in the Positron Theory’, Phys. Rev. 48, 55.
Van Dyck, R.S., Jr., P.B. Schwinberg, and H.G. Dehmelt: 1987, ‘New High-Precision Comparison of Electron and Positron g Factors’, Phys. Rev. Lett. 59, 26.
Walls, D.F.: 1979, ‘Evidence for the Quantum Nature of Light’, Nature 280, 451.
Weingard, R.: 1988, ‘Virtual Particles and the Interpretation of Quantum Field Theory’, in H.R. Brown and R. Harré (eds.), Philosophical Foundations of Quantum Field Theory, Clarendon Press, Oxford.
Weisskopf, V.: 1936, ‘Über die Elektrodynamik des vakuums auf grund der Quantentheorie des Elektrons’, Kon. Dan. Vid. Sel. Mat.-Fys. Medd. 15, No.6.
Weisskopf, V., and E.P. Wigner: 1930, ‘Linienbriete auf Grund der Diracschen Lichttheorie’, Z. Phys. 63, 54.
Welton, T.A.: 1948, ‘Some Observable Effects of the Quantum-Mechanical Fluctuations of the Electromagnetic Field’, Phys. Rev. 74, 1157.
Wentzel, G.: 1927, ‘Über die Richtungsverteilung der Photoelektronen’, Z. Phys. 41, 828.
Williams, R.C.: 1938, ‘The Fine Structures of Hα and Dα Under Varying Discharge Conditions’, Phys. Rev. 54, 558.
Wódkiewicz, K.: 1980, ‘Resonance Flourescence and Spontaneous Emission as Test of QED’, in A.O. Barut (ed.), Foundations of Radiation Theory and Quantum Electrodynamics, Plenum Press, New York.
Yennie, D.R., S.C. Frautschi, and H. Suura: 1961, ‘The Infrared Divergence Phenomena and High-Energy Processes’, Ann. Phys. (N.Y.) 13, 379.
Zwanziger, D.: 1979, ‘Infrared Catastrophe Averted by Hertz Potential’, Phys. Rev. D 19, 3614.
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Grandy, W.T. (1991). Quantum Theory of Radiation. In: Relativistic Quantum Mechanics of Leptons and Fields. Fundamental Theories of Physics, vol 41. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-3302-9_7
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