Abstract
New semiclassical models of virtual antiparticle pairs are used to compute the pair lifetimes, and good agreement with the Heisenberg lifetimes from quantum field theory (QFT) is found. The modeling method applies to both the electromagnetic and color forces. Evaluation of the action integral of potential field fluctuation for each interaction potential yields ≈ℏ/2 for both electromagnetic and color fluctuations, in agreement with QFT. Thus each model is a quantized semiclassical representation for such virtual antiparticle pairs, to good approximation. When the results of the new models and QFT are combined, formulae for e and α s (q) are derived in terms of only ℏ and c.
Similar content being viewed by others
REFERENCES
F. Brau, “Bohr-Sommerfeld quantization and meson spectroscopy,” Phys. Rev. D 62, 014005 (2000).
J. J. Sakurai, Advanced Quantum Mechanics (Addison-Wesley, Redwood City, California, 1967), p. 138. G. C. Wick, “Range of nuclear forces in Yukawa's theory,” Nature 142, 993 (1938). I. J. R. Aitchison, “Nothing's plenty, The vacuum in modern quantum field theory,” Contemp. Phys. 26(4), 333, in particular p. 369.
B. Hatfield, Quantum Field Theory of Point Particles and Strings (Addison-Wesley, Reading, Massachusetts, 1992), p. 407. P. W. Milonni, The Quantum Vacuum (Academic, San Diego, 1994), Chaps. 9 and 10.
E. P. Wigner, “On the time-energy uncertainty relation,” in Aspects in Quantum Theory, A. Salam and E. P. Wigner, eds. (Cambridge University Press, London, 1972). W. Greiner, “Opening remarks,” in Quantum Electrodynamics of Strong Fields (Plenum, New York, 1983), p. 6.
R. E. Langer, “On the connection formulas and the solutions of the wave equation,” Phys. Rev. 51, 669 (1938). H. C. von Baeyer, “Semiclassical quantization of the relativistic Kepler problem, ” Phys. Rev. D 12(10), 3086 (1975). B. Sheehy and H. C. von Baeyer, “Modified Bohr quantization of charmonium,” Am. J. Phys. 49(5), 429 (1981).
F. Gross, Relativistic Quantum Mechanics and Field Theory (Wiley Interscience, New York, 1993), p. 337. Also, see R. P. Feynman, “The reason for antiparticles,” in R. P. Feynman and S. Weinberg, Elementary Particles and the Laws of Physics (Cambridge University Press, Cambridge, 1987), p. 47.
V. B. Berestetski, E. M. Lifshitz, and L. P. Pitaevskii, Quantum Electrodynamics (Pergamon, Oxford, 1982), p. 3.
E. C. G. Stückelberg, “La mécanique du point matériel en théorie de la relativité et en théorie des quanta,” Helv. Phys. Acta 15, 23 (1942).
J. P. Costella, B. H. J. McKellar, and A. A. Rawlinson, “Classical antiparticles,” Am. J. Phys. 65, 835 (1997).
M. A. Trump and W. C. Schieve, Classical Relativistic Many-Body Dynamics (Kluwer Academic, Dordrecht, 1999), p. 24.
A. Carati, “Pair production in classical electrodynamics,” Found. Phys. 28, 843 (1998).
Cf. G. Baym, Lectures on Quantum Mechanics (Benjamin, New York, 1969), p. 518.
J. D. Jackson, Classical Electrodynamics, 2nd edn. (Wiley, New York, 1975), p. 185.
J. J. Sakurai, op. cit., p. 140.
For a review of positronium theory, see M. A. Stroscio, “Positronium: A review of the theory,” Phys. Reps. C22(5), 215 (1975).
J. D. Jackson, op. cit., pp. 553–555.
P. W. Milonni, op. cit., p. 403.
E.g., J. Huschilt, W. E. Baylis, D. Leiter, and G. Szamosi, “Numerical solutions to twobody problems in classical electrodynamics: straight-line motion with retarded fields and no radiation reaction,” Phys. Rev. D 7(10), 2844 (1973). J. C. Kasher, “Numerical solutions in classical relativistic electrodynamics: one-dimensional bound positronium,” J. Phys. A: Math. Gen 10(7), 1097 (1977).
J. J. Sakurai, op. cit., p. 118.
G. A. Korn and T. M. Korn, Mathematical Handbook for Scientists and Engineers, 2nd edn. (McGraw-Hill, New York, 1968), p. 974.
E. M. Purcell, Electricity and Magnetism (McGraw-Hill, New York, 1965), p. 365; J. D. Jackson, op. cit., p. 184.
See review by H. C. von Baeyer, op. cit.; also W. Dittrich and M. Reuter, Classical and Quantum Dynamics (Springer, Berlin, 1994).
D. Derbes, “Feynman's derivation of the Schrödinger equation,” Am. J. Phys. 64(7), 881 (1996).
C. Lanczos, The Variational Principles of Mechanics, 4th edn. (Dover, New York, 1986), p. 321.
F. Gross, op. cit., p. 478.
See review by W. Lucha, F. F. Schöberl, and D. Gromes, “Bound states of quarks,” Phys. Reps. 200(4), 127 (1991); in particular, p. 150.
D. B. Lichtenberg, The Standard Model Of Elementary Particles (Bibliopolis, Napoli, 1991), pp. 128–129.
S. Bethke, “Determination of the QCD coupling β,” J. Phys. G: Nucl. Part. Phys. 26, R27 (2000). F. Wilczek, “QCD made simple,” Phys. Today 53(8), 22 (2000).
K. G. Chetyrkin, B. A. Kniehl, and M. Steinhauser, “Strong coupling constant with flavor thresholds at four loops in the modified minimal-subtraction scheme,” Phys. Rev. Lett 79, 2184 (1997).
J. L. Richardson, “The heavy quark potential and the U, J/k systems,” Phys. Lett. 82B, 272 (1979).
S. Weinberg, The Quantum Theory of Fields III (Cambridge University Press, Cambridge, 1996), p. 152.
D. B. Lichtenberg, op. cit., p. 133.
V. Fitch, in Encycl. of Phys., 2nd edn. (VCH Publishers, New York, 1991), p. 1357; in particular, p. 1360.
K. Rith and A. Shäfer, “The mystery of nucleon spin,” Sci. Am. 281, 58 (1999).
See T. Y. Cao, Conceptual Developments of 20th Century Field Theories (Cambridge University Press, Cambridge, 1998), p. 198. J. Schwinger, “Quantum electrodynamics I: A covariant formulation,” Phys. Rev. 74, 1439 (1948). J. Schwinger, “Quantum Electrodynamics II: Vacuum polarization and self energy,” Phys. Rev. 75, 651 (1949).
K. Gottfried and V. F. Weisskopf, Concepts of Particle Physics, Volume II (Oxford University Press, New York, 1986), p. 263.
B. Hatfield, op. cit., p. 409.
G. Kane, The Particle Garden (Addison-Wesley, Reading, Massachusetts, 1995), p. 126.
N. A. Doughty, Lagrangian Interaction (Addison Wesley, Reading, Massachusetts, 1990), p. 24. J. A. Wheeler, in Battelle Rencontres: 1967 Lectures in Mathematics and Physics (Benjamin, New York, 1968), p. 269.
M. A. Oliver, “Classical electrodynamics of a point particle,” Found. Phys. 11, 61 (1998).
E.g., J. Barrow and F. Tipler, The Anthropic Principle (Oxford University Press, Oxford, 1986).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Batchelor, D. Semiclassical Models for Virtual Antiparticle Pairs, the Unit of Charge e, and the QCD Coupling α s . Foundations of Physics 32, 51–76 (2002). https://doi.org/10.1023/A:1013848830547
Issue Date:
DOI: https://doi.org/10.1023/A:1013848830547