Theories of the Fine Structure Constant α
Although the fine structure constant is one of the best determined numbers in physics, the reason why nature selects the particular value α = 1/137. 03602 ± 0. 00021 for the electromagnetic coupling strength is still a mystery, and has provoked much interesting theoretical speculation. For purposes of discussion, the speculations may be divided roughly into four general types: (a) Theories in which α is cosmologically determined; (b) Theories in which α is a constant which is determined microscopically through the interplay of the electromagnetic interaction with interactions of other types, either gravitational, weak or strong; (c) Theories in which α is microscopically determined through properties of the electromagnetic interaction alone, considered in isolation from other interactions; and (d) Numerological speculations.
KeywordsVacuum Polarization Renormalization Constant Fine Structure Constant Eigenvalue Condition Wave Function Renormalization
Unable to display preview. Download preview PDF.
- 2.L. D. Landau, On the Quantum Theory of Fields, in Niels Bohr and the Development of Physics, W. Pauli, ed. (Pergamon Press, London, 1955); B, S. DeWitt, PhySo Rev. Letters 13, 114 (1964); A. Salam and J. Strathdee, Nuovo Cimento Letters 4, 101 (1970).Google Scholar
- 3.For an excellent review see F. J0 Dyson, “The Fundamental Constants and their Time Variation”, Institute for Advanced Study preprint (1972).Google Scholar
- 5.J. Shechter and Y. Ueda, Phys. Rev. D2, 736 (1970); T. D. Lee, Phys. Rev. Letters 26, 801 (1971).Google Scholar
- 8.K. Johnson, M. Baker and R. Willey, Phys. Rev. 136B, 111 (1964); Ko Johnson, R. Willey and M. Baker, ibid 163, 1699 (1967); M. Baker and K. Johnson, ibid 183, 1292 (1969); M. Baker and K. Johnson, ibid D3, 2516, 2541 (1971).Google Scholar
- 9.Their result is based on an application of the Jost-Schroer- Federbush-Johnson theorem. See P. G. Federbush and K. Johnson, Phys. Rev. 120, 1296 (I960); and R. Jost, in Lectures on Field Theory and the Many-Body Problem, E. R. Caianiello, ed. ( Academic Press, N. Y., 1961 ).Google Scholar
- 10.S. Adler, “Short Distance Behavior of Quantum Electrodynamics and an Eigenvalue Condition for α”, Phys. Rev. (to be published).Google Scholar
- 12.Fourth order calculation: R. Jost and J. M. Luttinger, Helv. Phys. Acta 23, 201 (1950). Sixth order calculation: J. L. R. sner, Phys. Rev. Letters 17, 1190 (1966) and Ann. Phys. (N. Y.) 44, 11 (1967).Google Scholar
- 13.For a review of conformal invariance in field theory, see e. g. G. Mack and A. Salam, Ann. Phys. (N. Y.)53, 174(1969).Google Scholar
- 14.J. A. Wheeler (unpublished).Google Scholar
- 15.A. Wyler, C. Ro Acad. Sci., Ser.A 269, 743 (1969) and 271, 186 (1971). For discussions of this formula, see B. Robertson, Phys. Rev. Letters 27, 1545 (1971) and R. Gilmore, ibid 28, 462 (1972).Google Scholar