, Volume 97, Issue 1, pp 33–108 | Cite as

The conceptual foundations and the philosophical aspects of renormalization theory

  • Tian Yu Cao
  • Silvan S. Schweber


Conceptual Foundation Renormalization Theory Philosophical Aspect 
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  1. Adler, S. L.: 1969, ‘Axial-Vector Vertex in Spinor Electrodynamics’,Phys. Rev. 177, 2426–38.Google Scholar
  2. Aramaki, S.: 1989, ‘Development of the Renormalization Theory in Quantum Electrodynamics. II’,Historia Scientiarum 37, 91–113.Google Scholar
  3. Anderson, C. D.: 1932, ‘The Apparent Existence of Easily Deflectable Positives’,Science 76, 328–29.Google Scholar
  4. Appelquist, T., and J. Carazzone: 1975, ‘Infrared Singularities and Massive Fields’,Phys. Rev. D11, 2856–61.Google Scholar
  5. Arbib, M. A., and M. B. Hesse: 1986,The Construction of Reality, Cambridge University Press, Cambridge.Google Scholar
  6. Becchi, C., A. Rouet, and R. Stora: 1974, ‘The Abelian Higgs-Kibble Model, Unitarity of theS-operator’,Phys. Lett. 52B, 344–46.Google Scholar
  7. Bell, J. S.: 1964, ‘On the Einstein-Podolsky-Rosen Paradox,Physics 1, 195–200.Google Scholar
  8. Bell, J. S.: 1966, ‘On the Problem of Hidden Variables in Quantum Mechanics’,Rev. Mod. Phys. 38, 447–52.Google Scholar
  9. Bell, J. S.: 1987,Speakable and Unspeakable in Quantum Mechanics, Cambridge University Press, Cambridge.Google Scholar
  10. Bell, J. S., and R. Jackiw: 1969, ‘A PCAC Puzzle: π0 → γγ in the σ-model’,Nuovo Cim. 60A, 47–61.Google Scholar
  11. Bethe, H. A.: 1947, ‘The Electromagnetic Shift of Energy Levels’,Phys. Rev. 72, 339–41.Google Scholar
  12. Bjorken, J. D.: 1969, ‘Asymptotic Sum Rules at Infinite Momentum’,Phys. Rev. 179, 1547–53.Google Scholar
  13. Black, M.: 1962,Models and Metaphors, Cornell University Press, Ithaca.Google Scholar
  14. Bollinger, J. J., et al.: 1989, ‘Test of the Linearity of Quantum Mechanics by rf Spectroscopy of the9Beü Ground State’,Phys. Rev. Lett. 63(10), 1031–37.Google Scholar
  15. Bopp, F.: 1940, ‘Eine lineare Theorie des Elektrons’,Ann. Phys. 38, 345–84.Google Scholar
  16. Born, M.: 1926, ‘Zur Quantenmechnik der Stossvorgange’,Z. Phys. 37, 863–67.Google Scholar
  17. Born, M., W. Heisenberg, and P. Jordan: 1926, ‘Zur Quantenmechnik. II’,Z. Phys. 35, 557–615.Google Scholar
  18. Boulware, D.: 1970, ‘Renormalizability of Massive Non-Abelian Gauge Fields: A Functional Integral Approach’,Ann. Phys. 56, 140–71.Google Scholar
  19. Browder, F. E. (ed.): 1976,Mathematical Developments Arising from Hilbert Problems, Vol. 28, American Mathematical Society, Providence.Google Scholar
  20. Brouwer, L. E. J.: 1913, ‘Intuitionism and Formalism’,Bull. Amer. Math. Soc. (2)20, 61–69.Google Scholar
  21. Brown, L. M., and T. Y. Cao: 1991, ‘Spontaneous Breakdown of Symmetry: Its Rediscovery and Integration into Quantum Field Theory’,Historical Studies in the Physical and Biological Sciences 21, 211–35.Google Scholar
  22. Brown, L. M., M. Dresden, and L. Hoddeson (eds.): 1989,Pions to Quarks, Cambridge University Press, Cambridge.Google Scholar
  23. Brown, L. M., and L. Hoddeson (eds.): 1983,The Birth of Particle Physics, Cambridge University Press, Cambridge.Google Scholar
  24. Buchdahl, G.: 1970, ‘History of Science and Criteria of Choice’, in R. H. Stuewer (ed.),Historical and Philosophical Perspective of Science, University of Minnesota Press, Minneapolis, pp. 204–30.Google Scholar
  25. Buchdahl, G.: 1980, ‘Neo-transcendental Approaches towards Scientific Theory Appraisal’, in D. H. Mellor (ed.),Science, Belief and Behaviour, Cambridge University Press, Cambridge, pp. 1–21.Google Scholar
  26. Callan, C. G., Jr.: 1970, ‘Bjorken Scale Invariance in Scalar Field Theory’,Phys. Rev. D2, 1541–47.Google Scholar
  27. Cao, T. Y.: 1986, ‘A Conceptual History of Twentieth Century Field Theories’, Ph.D. dissertation, University of Cambridge (to be published by Cambridge University Press in 1993–94 asThe Conceptual Developments of Twentieth Century Field Theories).Google Scholar
  28. Cao, T. Y.: 1991, ‘The Reggeization Program 1962–1982: Attempts at Reconciling Quantum Field Theory withS-matrix Theory’,Archive for History of Exact Sciences 41, 239–83.Google Scholar
  29. Cartan, E.: 1922, ‘Sur une géneralisation de la notion de courbure de Riemann et les éspaces à torsion’,C. R. Ac. Sci. (Paris)174, 593.Google Scholar
  30. Cartwright, N.: 1983,How the Laws of Physics Lie, Oxford University Press, Oxford.Google Scholar
  31. Chevalley, C.: 1988, ‘Physical Reality and Closed Theories in Werner Heisenberg's Early Papers’, in D. Batens and J. P. van Bendegem (eds.),Theory Experiment. Recent Insights and New Perspectives on their Relations, D. Reidel, Dordrecht, pp. 159–76.Google Scholar
  32. Cohen, P. J.: 1963, ‘The Independence of the Continuum Hypothesis’,Proc. Natl. Acad. Sci. (U.S.A.) 50, 1143–48.Google Scholar
  33. Coleman, S.: 1986,Secret Symmetry, Cambridge University Press, Cambridge.Google Scholar
  34. Coleman, S., and E. Weinberg: 1973, ‘Radiative Corrections as the Origin of Spontaneous Symmetry Breaking’,Phys. Rev. D7, 1888–1910.Google Scholar
  35. Collins, J. C.: 1984,Renormalization, Cambridge University Press, Cambridge.Google Scholar
  36. Collins, J. C., F. Wilczek, and A. Zee: 1978, ‘Low-Energy Manifestations of Heavy Particles: Application to the Neutral Current’,Phys. Rev. D18, 242–47.Google Scholar
  37. Cushing, J. T.: 1990,Theory Construction and Selection in Modern Physics: The S-Matrix Theory, Cambridge University Press, Cambridge.Google Scholar
  38. Darrigol, O.: 1986, ‘The Origin of Quantized Matter Waves’,Historical Studies in the Physical and Biological Sciences 21, 197–253.Google Scholar
  39. Davies, P. (ed.): 1989,The New Physics, Cambridge University Press, Cambridge.Google Scholar
  40. Demopoulos, W., and M. Friedman: 1985, ‘The Analysis of Matter’,Philosophy of Science 52, 621–39.Google Scholar
  41. Dirac, P. A. M.: 1927a, ‘The Quantum Theory of Emission and Absorption of Radiation’,Proc. Roy. Soc. A114, 243–65.Google Scholar
  42. Dirac, P. A. M.: 1927b, ‘The Quantum Theory of Dispersion’,Proc. Roy. Soc. A114, 716–28.Google Scholar
  43. Dirac, P. A. M.: 1930, ‘A Theory of Electrons and Protons’,Proc. Roy. Soc. A126, 360–65.Google Scholar
  44. Dirac, P. A. M.: 1934, ‘Theorie du positron’, inRapport du 7e Conseil Solvay de Physique, Structure et Proprietes des noyaux atomiques (22–29 Oct. 1933), Gauthier-Villars, Paris, pp. 203–12.Google Scholar
  45. Dirac, P. A. M.: 1938, ‘Classical Theory of Radiating Electrons’,Proc. Roy. Soc. A167, 148–69.Google Scholar
  46. Dirac, P. A. M.: 1942, ‘The Physical Interpretation of Quantum Mechanics’,Proc. Roy. Soc. A180, 1–40.Google Scholar
  47. Dirac, P. A. M.: 1963, ‘The Evolution of the Physicist's Picture of Nature’,Scientific American 208, 45–53.Google Scholar
  48. Dirac, P. A. M.: 1969a, ‘Methods in Theoretical Physics’, inSpecial Suppl. of IAEA Bulletin, IAEA, Siena, pp. 21–28.Google Scholar
  49. Dirac, P. A. M.: 1969b, ‘Can Equations of Motion be Used’, inCoral Gables Conference on Fundamental Interactions at High Energy, Gordon and Breach, New York, pp. 1–18.Google Scholar
  50. Dirac, P. A. M.: 1973a, ‘Relativity and Quantum Mechanics’, in C. G. Sudarshan and Y. Neéman (eds.),The Past Decades in Particle Theory, Gordon and Breach, New York, pp. 741–72.Google Scholar
  51. Dirac, P. A. M.: 1973b, ‘Development of the Physicist's Conception of Nature’, in J. Mehra (ed.),The Physicist's Conception of Nature, D. Reidel, Dordrecht, pp. 1–14.Google Scholar
  52. Dirac, P. A. M.: 1977, ‘Recollections of an Exciting Era’, in C. Weiner (ed.),History of Twentieth Century Physics, Academic Press, New York, pp. 109–46.Google Scholar
  53. Dirac, P. A. M.: 1983, ‘The Origin of Quantum Field Theory’, in Brown, Dresden, and Hoddeson (1983), pp. 39–55.Google Scholar
  54. Duhem, P.: 1954,The Aim and Structure of Physical Theory, Princeton University Press, Princeton (originally published in 1906).Google Scholar
  55. Dyson, F. J.: 1949a, ‘The Radiation Theories of Tomonaga, Schwinger and Feynman’,Phys. Rev. 75, 486–502.Google Scholar
  56. Dyson, F. J.: 1949b, ‘TheS-matrix in Quantum Electrodynamics’,Phys. Rev. 75, 1736–55.Google Scholar
  57. Dyson, F. J.: 1951, ‘The Renormalization Method in Quantum Electrodynamics’,Proc. Roy. Soc. A207, 395–401.Google Scholar
  58. Dyson, F. J.: 1952, ‘Divergence of Perturbation Theory in Quantum Electrodynamics’,Phys. Rev. 85, 631–32.Google Scholar
  59. Einstein, A.: 1936, ‘Physics and Reality’,J. Franklin Inst. 221, 313–47.Google Scholar
  60. Essam, J. W., and M. E. Fisher: 1963, ‘Padé Approximant Studies of the Lattice Gas and Ising Ferromagnet below the Critical Point’,J. Chem. Phys. 38, 802–12.Google Scholar
  61. Fadeev, L. D., and V. N. Popov: 1967, ‘Feynman Diagrams for the Yang-Mills Field’,Phys. Lett. 25B, 29–30.Google Scholar
  62. Feldman, D.: 1949, ‘On Realistic Field Theories and the Polarization of the Vacuum’,Phys. Rev. 76, 1369–75.Google Scholar
  63. Feynman, R. P.: 1948a, ‘Space-time Approach to Non-relativistic Quantum Mechanics’,Rev. Mod. Phys. 20, 367–87.Google Scholar
  64. Feynman, R. P.: 1948b, ‘A Relativistic Cut-off for Classical Electrodynamics’,Phys. Rev. 74, 939–46.Google Scholar
  65. Feynman, R. P.: 1948c, ‘Relativistic Cut-off for Quantum Electrodynamics’,Phys. Rev. 74, 1430–38.Google Scholar
  66. Feynman, R. P.: 1949a, ‘The Theory of Positrons’,Phys. Rev. 76, 749–68.Google Scholar
  67. Feynman, R. P.: 1949b, ‘The Space-Time Approach to Quantum Electrodynamics’,Phys. Rev. 76, 769–89.Google Scholar
  68. Feynman, R. P.: 1963, ‘Quantum Theory of Gravity’,Acta Phys. Polonica 24, 697–722.Google Scholar
  69. Feynman, R. P.: 1973, ‘Partons’, in Sudarshan and Neéman (1973), p. 775.Google Scholar
  70. Feynman, R. P., and R. G. Hibbs: 1965,Quantum Mechanics and Path Integrals, McGraw-Hill, New York.Google Scholar
  71. Fisher, M. E.: 1964, ‘Correlation Functions and the Critical Region of Simple Fluids’,J. Math. Phys. 5, 944–62.Google Scholar
  72. Frenkel, J.: 1925, ‘Zur Elektrodynamik punktfoermiger Elektronen’,Z. Phys. 32, 518–34.Google Scholar
  73. Fritzsch, H., and P. Minkowski: 1975, ‘Unified Interactions of Leptons and Hadrons’,Ann. Phys. 93, 193–266.Google Scholar
  74. Freudenthal, G.: 1986,Atom and Individual in the Age of Newton, D. Reidel, Boston.Google Scholar
  75. Furry, W. H., and J. R. Oppenheimer: 1934, ‘On the Theory of the Electron and Positron’,Phys. Rev. 45, 245–62.Google Scholar
  76. Gasiorowicz, S. G., P. R. Yennie, and H. Suura: 1959, ‘Magnitude of Renormalization Constants’,Phys. Rev. Lett. 2, 513–16.Google Scholar
  77. Gell-Mann, M.: 1987, ‘Particle Theory fromS-matrix to Quark’, in M. G. Doncel, A. Hermann, L. Michel, and A. Pais (eds.),Symmetries in Physics (1600–1980), Bellaterra, Barcelona, pp. 474–97.Google Scholar
  78. Gell-Mann, M.,: 1989, ‘Progress in Elementary Particle Theory, 1950–1964’, in Brown, Dresden, and Hoddeson (1989), pp. 694–711.Google Scholar
  79. Gell-Mann, M., and F. E. Low: 1954, ‘Quantum Electrodynamics at Small Distances’,Phys. Rev. 95, 1300–12.Google Scholar
  80. Gell-Mann, M., and Y. Neéman: 1964,The Eightfold Way, Benjamin, New York.Google Scholar
  81. Georgi, H.: 1989a, ‘Grand Unified Field Theories’, in Davies (1989), pp. 425–45.Google Scholar
  82. Georgi, H.: 1989b, ‘Effective Quantum Field Theories’, in Davies (1989), pp. 446–57.Google Scholar
  83. Georgi, H., and S. L. Glashow: 1974, ‘Unity of all Elementary Particles’,Phys. Rev. Lett. 32, 438–41.Google Scholar
  84. Georgi, H., H. Quinn, and S. Weinberg: 1974, ‘Hierarchy of Interactions in Unified Gauge Theories’,Phys. Rev. Lett. 33, 451–54.Google Scholar
  85. Gödel, K.: 1931, ‘Über formal unentscheibare Sätze der Principia Mathematica und verwandter Systeme. I’,Mh. Math. Phys. 38, 173–98.Google Scholar
  86. Gödel, K.: 1938, ‘The Consistency of the Axiom of Choice and of the Generalized Continuum-Hypothesis’,Proc. Natl. Acad. Sci. (U.S.A.) 24, 556–57.Google Scholar
  87. Gödel, K.: 1939, ‘Consistency-Proof for the Generalized Continuum-Hypothesis’,Proc. Natl. Acad. Sci. (U.S.A.) 25, 220–24.Google Scholar
  88. Gödel, K.: 1940, ‘The Consistency of the Continuum Hypothesis’,Ann. Math. Stud., No. 3.Google Scholar
  89. Gödel, K.: 1947, ‘What is Cantor's Continuum Problem?’,Am. Math. Mon. 54, 515–25.Google Scholar
  90. Green, M. B., J. H. Schwarz, and E. Witten: 1987,Superstring Theory, Cambridge University Press, Cambridge.Google Scholar
  91. Gross, D.: 1985, ‘Beyond Quantum Field Theory’, in J. Ambjorn, B. J. Durhuus, and J. L. Petersen (eds.),Recent Developments in Quantum Field Theory, North-Holland, Amsterdam, pp. 151–68.Google Scholar
  92. Gross, D., and F. Wilczek: 1973a, ‘Ultraviolet Behavior of Non-Abelian Gauge Theories’,Phys. Rev. Lett. 30, 1343–46.Google Scholar
  93. Gross, D., and F. Wilczek: 1973b, ‘Asymptotically Free Gauge Theories: I’,Phys. Rev. D8, 3633–52.Google Scholar
  94. Hacking, I.: 1983,Representing and Interpreting, Cambridge University Press, Cambridge.Google Scholar
  95. Harman, P. M.: 1982a,Energy, Force, and Matter. The Conceptual Development of Nineteenth-Century Physics, Cambridge University Press, Cambridge.Google Scholar
  96. Harman, P. M.: 1982b,Metaphysics and Natural Philosophy. The Problem of Substance in Classical Physics, Barnes and Noble, Totowa, N.J.Google Scholar
  97. Hawking, S.: 1980,Is the End in Sight for Theoretical Physics?, Cambridge University Press, Cambridge.Google Scholar
  98. Heisenberg, W.: 1934, ‘Bemerkung zur Diracschen Theorie des Positrons’,Z. Phys. 90, 209–31.Google Scholar
  99. Heisenberg, W.: 1960, ‘Recent Research on the Nonlinear Spinor Theory of Elementary Particles’, inProceedings of International Annual Conference on High Energy Physics, University of Rochester, Rochester.Google Scholar
  100. Heisenberg, W.: 1966,Introduction to the Unified Field Theory of Elementary Particles, Interscience Publishers, London.Google Scholar
  101. Heisenberg, W.: 1974,Across the Frontiers, Harper and Row, New York.Google Scholar
  102. Heisenberg, W., and W. Pauli: 1929, ‘Zur Quantentheorie der Wellenfelder’,Z. Phys. 56, 1–61.Google Scholar
  103. Heitler, W.: 1961, in R. Stoops (ed.),The Quantum Theory of Fields, Interscience Publishers, London.Google Scholar
  104. Hesse, M. B.: 1962,Forces and Fields, Philosophical Library, New York.Google Scholar
  105. Hesse, M. B.: 1963,Models and Analogies in Science, Sheed and Ward, London.Google Scholar
  106. Hesse, M. B.: 1965, ‘The Explanatory Function of Metaphor’, in Y. Bar-Hillel (ed.),Logic, Methodology and Philosophy of Science, North-Holland, Amsterdam, pp. 249–59.Google Scholar
  107. Hesse, M. B.: 1974,The Structure of Scientific Inference, MacMillan, London.Google Scholar
  108. Hesse, M. B.: 1980,Revolutions and Reconstructions in the Philosophy of Science, Harvester, Brighton-Sussex.Google Scholar
  109. Hilbert, D.: 1900, ‘Mathematical Problems’, inGottingen Nachr. 253–97 (trans. in: 1902,Bull. Amer. Math. Soc. 8, 437–79).Google Scholar
  110. Hilbert, D.: 1918, ‘Axiomatisches Denken’,Math. Ann. 78, 405–515.Google Scholar
  111. Hilbert, D.: 1930, ‘Probleme der Grundlagung der Mathematik’,Math. Ann. 102, 1–9.Google Scholar
  112. Hilbert, D., and P. Bernays: 1939,Grundlagen der Mathematik, Vol. 2, Springer-Verlag, Berlin.Google Scholar
  113. Hurst, C. A.: 1952, ‘The Enumeration of Graphs in the Feynman-Dyson Technique’,Proc. Roy. Soc. A214, 44–61.Google Scholar
  114. Jackiw, R.: 1972, ‘Field Investigations in Current Algebra’, in S. B. Treiman, R. Jackiw, and D. J. Gross (eds.),Lectures on Current Algebra and Its Applications, Princeton University Press, Princeton, pp. 97–254.Google Scholar
  115. Jaffe, A.: 1965, ‘Divergence of Perturbation Theory for Bosons’,Commun. Math. Phys. 1, 127–49.Google Scholar
  116. Johnson, K.: 1961, ‘Solution of the Equations for the Green's Functions of a Two Dimensional Relativistic Field Theory’,Nuovo Cim. 20, 773–90.Google Scholar
  117. Jordan, P., and O. Klein: 1927, ‘Zum Mehrkörperproblem der Quantentheorie’,Z. Phys. 45, 751–65.Google Scholar
  118. Jordan, P., and E. Wigner: 1928, ‘Über das Paulische Equivalenzverbot’,Z. Phys. 47, 631–51.Google Scholar
  119. Jost, R.: 1965,The General Theory of Quantum Fields, American Mathematical Society, Providence.Google Scholar
  120. Kadanoff, L. P.: 1966, ‘Scaling Laws for Ising Models nearT c’,Physics 2, 263–72.Google Scholar
  121. Källen, G.: 1953, ‘On the Magnitude of the Renormalization Constants in Quantum Electrodynamics’,Dan. Mat.-Fys. Medd. 27, 1–18.Google Scholar
  122. Källen, G.: 1966, ‘Review of Consistency Problems in Quantum Electrodynamics’,Acta Phys. Austr. Suppl. II, 133–61.Google Scholar
  123. Kamefuchi, S.: 1951, ‘Note on the Direct Interaction between Spinor Fields’,Progr. Theor. Phys. 6, 175–81.Google Scholar
  124. Klein, F.: 1872,Vergleichende Betrachtungen über neuere geometrische Forschungen, Deichert, Erlangen.Google Scholar
  125. Klein, F.: 1918, ‘Über die Differentialgesetze für die Erhaltung von Impuls und Energie in der Einsteinschen Gravitationstheorie’,Nachr. Ges. Wiss. Gott. Math. Phys. Kl. 171–89.Google Scholar
  126. Körner, S.: 1960,The Philosophy of Mathematics, Hutchinson University Library, London.Google Scholar
  127. Kramers, H.: 1938,Quantentheorie des Elektrons und der Strahlung, Akad. Verlag, Leipzig (trans. D. ter Haar: 1957, North-Holland, Amsterdam).Google Scholar
  128. Kreisel, G.: 1976, ‘What have we learnt from Hilbert's Second Problem?’, in Browder, (1976), pp. 93–130.Google Scholar
  129. Kreisel, G.: 1980, ‘Kurt Gödel’, inBiographical Memoirs of Fellows of the Royal Society (London)26, 149–224.Google Scholar
  130. Lamb, W. E., Jr., and R. C. Retherford: 1947, ‘Fine Structure of the Hydrogen Atom by a Microwave Method’,Phys. Rev. 72, 241–43.Google Scholar
  131. Landau, L. D.: 1955, ‘On the Quantum Theory of Fields’, in W. Pauli (ed.),Niels Bohr and the Development of Physics, Pergamon, London, pp. 52–69.Google Scholar
  132. Landau, L. D., A. A. Abrikosov, and I. M. Khalatnikov: 1954a, ‘The Removal of Infinities in Quantum Electrodynamics’,Doklady 95, 497–99.Google Scholar
  133. Landau, L. D., A. A. Abrikosov, and I. M. Khalatnikov: 1954b, ‘An Asymptotic Expression for the Electron Green Function in Quantum Electrodynamics’,Doklady 95, 773–76.Google Scholar
  134. Landau, L. D., A. A. Abrikosov, and I. M. Khalatnikov: 1954c, ‘An Asymptotic Expression for the Photon Green Function in Quantum Electrodynamics’,Doklady 95, 1117–20.Google Scholar
  135. Landau, L. D., A. A. Abrikosov, and I. M. Khalatnikov: 1954d, ‘The Electron Mass in Quantum Electrodynamics’,Doklady 96, 261–63.Google Scholar
  136. Landau, L. D., A. A. Abrikosov, and I. M. Khalatnikov: 1956, ‘On the Quantum Theory of Fields’,Nuovo Cimento Suppl. 3, 80–104.Google Scholar
  137. Landau, L. D., and I. Pomeranchuck: 1955, ‘On Point Interactions in Quantum Electrodynamics’,Doklady 102, 489–91.Google Scholar
  138. Lee, B. W., and J. Zinn-Justin: 1972, ‘Spontaneously Broken Gauge Symmetries’,Phys. Rev. D5, 3121–60.Google Scholar
  139. Lepage, G. P.: 1989, ‘What is Renormalization?’, preprint, CLNS, 89–970, Newman Lab. of Nuclear Studies, Cornell University.Google Scholar
  140. Lewis, H. W.: 1948, ‘On the Reactive Terms in Quantum Electrodynamics’,Phys. Rev. 73, 173–76.Google Scholar
  141. Lie, S., and F. Engel: 1893,Theorie der Transformationsgruppen, Vol. 3, B. G. Teubner, Leipzig.Google Scholar
  142. Lorentz, H. A.: 1904a, ‘Maxwells elektromagnetische Theorie’, inEncyc. Mat. Wiss. V(2), 63–144.Google Scholar
  143. Lorentz, H. A.: 1904b, ‘Weiterbildung der Maxwellschen Theorie: Elektronentheorie’, inEncyc. Mat. Wiss. V(2), 145–280.Google Scholar
  144. Mack, G.: 1968, ‘Partially Conserved Dilatation Current’,Nucl. Phys. B5, 499–507.Google Scholar
  145. Maxwell, G.: 1970, ‘Structural Realism and the Meaning of Theoretical Terms’, in M. Radewer and S. Winokur (eds.),Analyses of Theories and Methods of Physics and Psychology, Vol. 8, Minnesota Studies in the Philosophy of Science, University of Minnesota Press, Minneapolis, pp. 181–92.Google Scholar
  146. Mehra, J. (ed.): 1973,The Physicist's Conception of Nature, D. Reidel, Dordrecht.Google Scholar
  147. Mills, R. L., and C. N. Yang: 1966, ‘Treatment of Overlapping Divergences in the Photon Self-Energy Function’,Progr. Theor. Phys. Suppl. 37–38, 507–11.Google Scholar
  148. Milne, E. A.: 1929,The Aim of Mathematical Physics, Oxford University Press, Oxford.Google Scholar
  149. Minkowski, H.: 1908, ‘Die Grundgleichungen für die elektromagnetischen Vorguge in bewegten Körper’,Gott. Nachr. 53–111.Google Scholar
  150. Minkowski, H.: 1909, ‘Raum und Zeit’,Phyz. Ztschr. 10, 104–11.Google Scholar
  151. Nafe, J. E., E. B. Nelson, and I. I. Rabi: 1947, ‘The Hyperfine Structure of Atomic Hydrogen and Deuterium’,Phys. Rev. 71, 914–15.Google Scholar
  152. Oppenheimer, J. R.: 1930, ‘Note on the Interaction of Field and Matter’,Phys. Rev. 35, 461–77.Google Scholar
  153. Pais, A.: 1945, ‘On the Theory of the Electron and of the Nucleon’,Phys. Rev. 68, 227–28.Google Scholar
  154. Pauli, W., and F. Villars: 1949, ‘On the Invariant Regularization in Relativistic Quantum Theory’,Rev. Mod. Phys. 21, 434–44.Google Scholar
  155. Pauli, W., and V. Weisskopf: 1934, ‘Über die Quantisierung der skalaren relativistischen Wellengleichung’,Helv. Phys. Acta 7, 709–31.Google Scholar
  156. Peierls, R.: 1934, ‘The Vacuum in Dirac's Theory of the Positive Electron’,Proc. Roy. Soc. A146, 420–41.Google Scholar
  157. Peterman, A.: 1953, ‘Divergence of Perturbation Expression’,Phys. Rev. 89, 1160–61.Google Scholar
  158. Peterman, A.: 1953, ‘Renormalisation dans les séries divergentes’,Helv. Phys. Acta 26, 291–99.Google Scholar
  159. Peterman, A., and E. C. G. Stueckelberg: 1951, ‘Restriction of Possible Interactions in Quantum Electrodynamics’,Phys. Rev. 82, 548–49.Google Scholar
  160. Pfeuti, P., and G. Toulouse: 1977,Introduction to the Renormalization Group and Critical Phenomena, Wiley, New York.Google Scholar
  161. Poincaré, H.: 1906, ‘Sur la dynamique de l'électron’,Read. Circ. Mat. Palermo 21, 129–75.Google Scholar
  162. Polchinski, J.: 1984, ‘Renormalization and Effective Lagrangians’,Nucl. Phys. B231, 269–95.Google Scholar
  163. Polchinski, J.: 1991: ‘Weinberg's Nonlinear Quantum Mechanics and the Einstein-Podolsky-Rosen Paradox’,Phys. Rev. Lett. 66(4), 397–401.Google Scholar
  164. Politzer, H.: 1973, ‘Reliable Perturbative Results for Strong Interactions?’,Phys. Rev. Lett. 30, 1346–49.Google Scholar
  165. Popper, K.: 1970, ‘A Realist View of Logic, Physics, and History’, in W. Yourgrau and A. D. Breck (eds.),Physics, Logic, and History, Plenum, New York, pp. 1–39.Google Scholar
  166. Putnam, H.: 1977,Meaning and the Moral Sciences, Routledge and Kegan Paul, London.Google Scholar
  167. Radicati, L. A.: 1984, ‘Chaos and Cosmos’, in I. Bars, A. Chodos and C.-H. Tze (eds.),Particle Physics, Plenum, New York, pp. 33–45.Google Scholar
  168. Rayski, J.: 1948, ‘On Simultaneous Interaction of Several Fields and the Self-energy Problem’,Acta Phys. Polonica 9, 129–40.Google Scholar
  169. Reichenbach, H.: 1938,Experience and Prediction, University of Chicago Press, Chicago.Google Scholar
  170. Reichenbach, H.: 1951,The Rise of Scientific Philosophy, University of California Press, Berkeley.Google Scholar
  171. Reines, F.: 1989, ‘Detection of the Neutrino’, in Brown, Dresden, and Hoddeson (1989), pp. 359–66.Google Scholar
  172. Rivier, D., and E. C. G. Stueckelberg: 1948, ‘A Convergent Expression for the Magnetic Moment of the Neutron’,Phys. Rev. 74, 218.Google Scholar
  173. Rohrlich, F.: 1973, ‘The Electron: Development of the First Elementary Particle Theory’, in Mehra (1973), pp. 331–69.Google Scholar
  174. Russell, B.: 1914,Our Knowledge of the External World as a Field for Scientific Method in Philosophy, Allen and Unwin, London.Google Scholar
  175. Russell, B.: 1927,The Analysis of Matter, Allen and Unwin, London.Google Scholar
  176. Sakata, S.: 1947, ‘The Theory of the Interaction of Elementary Particles’,Progr. Theor. Phys. 2, 145–47.Google Scholar
  177. Sakata, S.: 1950, ‘On the Direction of the Theory of Elementary Particles’,Iwanami II, 100–03 (English trans.: 1971,Progr. Theor. Phys. Suppl. 50, 155-58).Google Scholar
  178. Sakata, S.: 1956, ‘On a Composite Model for the New Particles’,Progr. Theor. Phys. 16, 686–88.Google Scholar
  179. Sakata, S., and O. Hara: 1947, ‘The Self-energy of the Electron and the Mass Difference of Nucleons’,Progr. Theor. Phys. 2, 30–31.Google Scholar
  180. Sakata, S., and H. Umezawa: 1950, ‘On the Applicability of the Method of Mixed Fields in the Theory of the Elementary Particles’,Progr. Theor. Phys. 5, 682–91.Google Scholar
  181. Sakata, S., H. Umezawa, and S. Kamefuchi: 1952, ‘On the Structure of the Interaction of the Elementary Particles’,Progr. Theor. Phys. 7, 377–90.Google Scholar
  182. Salam, A.: 1951a, ‘Overlapping Divergences and the S-matrix’,Phys. Rev. 82, 217–27.Google Scholar
  183. Salam, A.: 1951b, ‘Divergent Integrals in Renormalizable Field Theories’,Phys. Rev. 84, 426–31.Google Scholar
  184. Salam, A.: 1968, ‘Weak and Electromagnetic Interactions’, inProceedings of Nobel Conference VIII, Almquist and Wiskell, Stockholm, pp. 367–77.Google Scholar
  185. Salam, A.: 1973, ‘Progress in Renormalization Theory since 1949’, in Mehra (1973), pp. 430–46.Google Scholar
  186. Salam, A., and J. Strathdee: 1970, ‘Quantum Gravity and Infinities in Quantum Electrodynamics’,Lett. Nuovo Cim. 4, 101–08.Google Scholar
  187. Schlick, M.: 1918,General Theory of Knowledge, trans. A. E. Blumberg and H. Feigl, Springer-Verlag, New York.Google Scholar
  188. Schnitzer, H. J.: 1988, ‘The Crucial Calculation as a Motivating Force in Particle Physics’, Joint Seminar for the History and Philosophy of Science, Harvard University, Cambridge.Google Scholar
  189. Schweber, S. S.: 1985, ‘A Short History of Shelter Island I’, in R. Jackiw, N. N. Khuri, S. Weinberg, and E. Witten (eds.),Shelter Island I, MIT Press, Cambridge, pp. 301–43.Google Scholar
  190. Schweber, S. S.: 1986a, ‘Shelter Island, Pocono, and Oldstone: The Emergence of American Quantum Electrodynamics after World War II’,Osiris, 2nd Ser.2, 265–302.Google Scholar
  191. Schweber, S. S.: 1986b, ‘Feynman and the Visualization of Spacetime Processes’,Rev. Mod. Physics 58, 449–508.Google Scholar
  192. Schweber, S. S.: 1989, ‘Molecular Beams Experiments, the Lamb Shift, and the Relation between Experiments and Theory’,Amer. J. Phys. 57, 299–308.Google Scholar
  193. Schweber, S. S.: 1993, ‘Changing Conceptualizations of Renormalization Theory’, in L. Brown (ed.),Renormalization Theory, Springer-Verlag, New York.Google Scholar
  194. Schweber, S. S., H. A. Bethe, and F. de Hoffmann: 1955,Mesons and Fields, Vol. I, Row, Peterson and Co., Evanston, IL.Google Scholar
  195. Schwinger, J.: 1948a, ‘On Quantum Electrodynamics and the Magnetic Moment of the Electron’,Phys. Rev. 73, 416–17.Google Scholar
  196. Schwinger, J.: 1948b, ‘Quantum Electrodynamics. I. A Covariant Formulation’,Phys. Rev. 74, 1439–61.Google Scholar
  197. Schwinger, J.: 1951, ‘On the Green's Functions of Quantized Field. I’,Proc. Natl. Acad. Sci. (U.S.A.) 37, 452–59.Google Scholar
  198. Schwinger, J.: 1970,Particles, Sources and Fields, Vol. I, Addison-Wesley, Reading.Google Scholar
  199. Schwinger, J.: 1973, ‘A Report on Quantum Electrodynamics’, in Mehra (1973), pp. 413–29.Google Scholar
  200. Schwinger, J.: 1983, ‘Renormalization Theory of Quantum Electrodynamics: An Individual View’, in Brown and Hoddeson (1983), pp. 329–53.Google Scholar
  201. Shimony, A.: 1987, ‘Methodology of Synthesis: Parts and Wholes in Low Energy Physics’, in K. Kargon and P. Achinstein (eds.),Kelvin's Baltimore Lectures and Modern Theoretical Physics, MIT Press, Cambridge, pp. 399–423.Google Scholar
  202. Shimony, A.: 1992, ‘Reality, Causality, and Closing the Circle’, in hisSearch for a Naturalistic World View, Vol. 1, Cambridge University Press, Cambridge, pp. 21–61.Google Scholar
  203. Streater, R. F., and A. S. Wightman: 1964,PTC, Spin and Statistics, and All That, Benjamin, Reading.Google Scholar
  204. Stueckelberg, E. C. G.: 1938, ‘Die Wechselwirkungskrafte in der Elektrodynamik und in der Feldtheorie der Kernkrafte’,Helv. Phys. Acta 11, 225–44, 299–329.Google Scholar
  205. Stueckelberg, E. C. G., and A. Peterman: 1953, ‘La normalisation des constantes dans la theorie des quanta’,Helv. Phys. Acta 26, 499–520.Google Scholar
  206. Sudarshan, L. G., and Y. Neéman (eds.): 1973,The Past Decade in Particular Theory, Gordon and Breach, London.Google Scholar
  207. Symanzik, K.: 1970, ‘Small Distance Behavior in Field Theory and Power Counting’,Commun. Math. Phys. 18, 227–46.Google Scholar
  208. Symanzik, K.: 1973, ‘Infrared Singularities and Small-Distance-Behavior Analysis’,Commun. Math. Phys. 34, 7–36.Google Scholar
  209. Symanzik, K.: 1983, ‘Continuum Limit and Improved Action in Lattice Theories’,Nucl. Phys. B226, 187–227.Google Scholar
  210. Takabayasi, T.: 1983, ‘Some Characteristic Aspects of Early Elementary Particle Theory in Japan’, in Brown and Hoddeson (1983), pp. 294–303.Google Scholar
  211. Taketani, M.: 1942, ‘On Formation of the Newton Mechanics’,Kagaku, August (trans.: 1971,Progr. Theor. 50, 53–64).Google Scholar
  212. Teller, P.: 1988, ‘Three Problems of Renormalization’, in H. R. Brown and R. Harré (eds.),Philosophical Foundations of Quantum Field Theory, Clarendon Press, Oxford, pp. 73–89.Google Scholar
  213. Thirring, W.: 1953, ‘On the Divergence of Perturbation Theory for Quantum Fields’,Helv. Phys. Acta 26, 33–52.Google Scholar
  214. Thomson, J. J.: 1881, ‘On the Electric and Magnetic Effects Produced by the Motion of Electrified Bodies’,Phil. Mag. 11, 227–49.Google Scholar
  215. 't Hooft, G.: 1971a, ‘Renormalization of Massless Yang-Mills Fields’,Nucl. Phys. B33, 173–99.Google Scholar
  216. 't Hooft, G.: 1971b, ‘Renormalizable Lagrangians for Massive Yang-Mils Fields’,Nucl. Phys. B35, 167–88.Google Scholar
  217. 't Hooft, G., and M. Veltman: 1972a, ‘Renormalization and Regularization of Gauge Fields’,Nucl. Phys. B44, 189–213.Google Scholar
  218. 't Hooft, G., and M. Veltman: 1972b, ‘Combinatorics of Gauge Fields’,Nucl. Phys. B50, 318–53.Google Scholar
  219. 't Hooft, G., and M. Veltman: 1972c, ‘Example of Gauge Field Theory’, in C. Korthals-Altes (ed.),Renormalization of Yang-Mills Fields and Applications to Particle Physics, CNRS, Marseille.Google Scholar
  220. Tomonaga, S.: 1946, ‘On a Relativistically Invariant Formulation of the Quantum Theory of Wave Fields’,Progr. Theor. Phys. 1, 27–42.Google Scholar
  221. Tomonaga, S.: 1965, ‘Development of Quantum Electrodynamics’, inNoble Lectures (Physics): 1963–1970, Elsevier, Amsterdam, pp. 126–36.Google Scholar
  222. Umezawa, H. and R. Kawabe: 1949a, ‘Some General Formulae Relating to Vacuum Polarization’,Progr. Theor. Phys. 4, 423–42.Google Scholar
  223. Umezawa, H., and R. Kawabe: 1949b, ‘Vacuum Polarization due to Various Charged Particles’,Progr. Theor. Phys. 4, 443–60.Google Scholar
  224. Umezawa, H., J. Yukawa, and E. Yamada: 1948, ‘The Problem of Vacuum Polarization’,Progr. Theor. Phys. 3, 317–18.Google Scholar
  225. Van Fraassen, B.: 1980,The Scientific Image, Oxford University Press, New York.Google Scholar
  226. Velo, G. and A. Wightman (eds.): 1973,Constructive Quantum Field Theory, Springer-Verlag, Berlin.Google Scholar
  227. Veltman, M.: 1968a, ‘Relation between the Practical Results of Current Algebra Techniques and the Originating Quark Model’, Copenhagen Lectures, July 1968 (repr. in: R. Akhoury, B. De Wit, P. van Nieuwenhuizen, and M. Veltman (eds.): 1992,Gauge Theory — Past and Future, World Scientific, Singapore).Google Scholar
  228. Veltman, M.: 1968b, ‘Perturbation Theory of Massive Yang-Mills Fields’,Nucl. Phys. B7, 637–50.Google Scholar
  229. Veltman, M.: 1969a,Proc. Topical Conf. on Weak Interactions, CERN Yellow Report, 69-7, CERN, Geneva.Google Scholar
  230. Veltman, M. (with J. Reiff): 1969b, ‘Massive Yang-Mills Fields’,Nucl. Phys. B13, 545–64.Google Scholar
  231. Veltman, M.: 1970, ‘Generalized Ward Identities and Yang-Mills Fields’,Nucl. Phys. B21, 288–302.Google Scholar
  232. Veltman, M.: 1977, ‘Large Higgs Mass and μ-e Universality’,Phys. Lett. 70B, 253–54.Google Scholar
  233. Waller, I.: 1930, ‘Bemerküngen über die Rolle der Eigenenergie des Elektrons in der Quantentheorie der Strahlung’,Z. Phys. 62, 673–76.Google Scholar
  234. Ward, J. C.: 1950, ‘An Identity in Quantum Electrodynamics’,Phys. Rev. 78, 182.Google Scholar
  235. Ward, J. C.: 1951, ‘On the Renormalization of Quantum Electrodynamics’,Proc. Phys. Soc. (London)A64, 54–56.Google Scholar
  236. Weinberg, S.: 1960, ‘High Energy Behavior in Quantum Field Theory’,118, 838–49.Google Scholar
  237. Weinberg, S.: 1967, ‘A Model of Leptons’,Phys. Rev. Lett. 19, 1264–66.Google Scholar
  238. Weinberg, S.: 1978, ‘Critical Phenomena for Field Theorists’, in A. Zichichi (eds.),Understanding the Fundamental Constituents of Matter, Plenum, New York, pp. 1–52.Google Scholar
  239. Weinberg, S.: 1979, ‘Phenomenological Lagrangians’,Physica 96A, 327–40.Google Scholar
  240. Weinberg, S.: 1980a, ‘Conceptual Foundations of the Unified Theory of Weak and Electromagnetic Interactions’,Rev. Mod. Phys. 52, 515–23.Google Scholar
  241. Weinberg, S.: 1980b, ‘Effective Gauge Theorie’,Phys. Lett. 91B, 51–55.Google Scholar
  242. Weinberg, S.: 1983, ‘Why the Renormalization Group is a Good Thing’, in A. H. Guth, K. Huang, and R. L. Jaffee (eds.),Asymptotic Realms of Physics: Essays in Honor of Francis E. Low, MIT Press, Cambridge, pp. 1–19.Google Scholar
  243. Weinberg, S.: 1989a, ‘Precision Tests of Quantum Mechanics’,Phys. Rev. Lett. 62(5), 485–88.Google Scholar
  244. Weinberg, S.: 1989b, ‘Testing Quantum Mechanics’,Annals of Physics 194, 336–86.Google Scholar
  245. Weisskopf, V. F.: 1934, ‘Über die Selbstenergie des Elektrons’,Z. Phys. 89, 27–39.Google Scholar
  246. Weisskopf, V. F.: 1936, ‘Über die Elektrodynamic des Vakuums auf Grund der Quantentheorie des Elektrons’,K. Danske Vidensk. Selsk., Math.-Fys. Medd. 14, 1–39.Google Scholar
  247. Weisskopf, V. F.: 1939, ‘On the Self-energy and the Electromagnetic Field of the Electron’,Phys. Rev. 56, 72–85.Google Scholar
  248. Weisskopf, V. F.: 1983, ‘Growing up with Field Theory: The Development of Quantum Electrodynamics’, in Brown and Hoddeson (1983), pp. 56–81.Google Scholar
  249. Wentzel, G.: 1943,Einfuhrung in die Quantentheorie der Wellenfelfer, F. Deuticke, Wein.Google Scholar
  250. Weyl, H.: 1918a,Raum. Zeit. Materie, J. Springer, Berlin.Google Scholar
  251. Weyl, H.: 1918b, ‘Gravitation und Elektrizität’,Sitzber. Preuss. Akad. Wiss. 465.Google Scholar
  252. Weyl, H.: 1929, ‘Elektron und Gravitation’,Z. Phys. 56, 330–52.Google Scholar
  253. Whitehead, A. N., and B. Russell: 1910–13,Principia Mathematica, 3 vols., Cambridge University Press, Cambridge.Google Scholar
  254. Widom, B.: 1965a, ‘Surface Tension and Molecular Correlations near the Critical Point’,J. Chem. Phys. 43, 3892–97.Google Scholar
  255. Widom, B.: 1965b, ‘Equation of State in the Neighborhood of the Critical Point’,J. Chem. Phys. 43, 3898–3905.Google Scholar
  256. Wightman, A. S.: 1976, ‘Hilbert's Sixth Problem: Mathematical Treatment of the Axioms of Physics’, in Browder (1976), pp. 147–240.Google Scholar
  257. Wightman, A. S.: 1978, ‘Field Theory, Axiomatic’, inEncyclopedia of Physics, McGraw-Hill, New York, pp. 318–21.Google Scholar
  258. Wightman, A. S.: 1986, Some Lessons of Renormalization Theory’, in J. de Boer, E. Dal, and D. Ulfbeck (eds.),The Lesson of Quantum Theory, Elsevier Science B.V., Amsterdam, pp. 201–25.Google Scholar
  259. Wightman, A. S.: 1989, ‘The General Theory of Quantized Fields in the 1950s’, in Brown, Dresden, and Hoddeson (1989), pp. 608–29.Google Scholar
  260. Wigner, E.: 1931,Gruppentheorie und ihre Anwendung auf die Quantenmechanik der Atomspektren, F. Vieweg, Braunschweig.Google Scholar
  261. Wigner, E.: 1937, ‘On the Consequences of the Symmetry of the Nuclear Hamiltonian on the Spectroscopy of Nuclei’,Phys. Rev. 51, 106–19.Google Scholar
  262. Wigner, E.: 1960, ‘The Unreasonable Effectiveness of Mathematics in the Natural Sciences’,Com. Pure Appl. Math. 13, 1–14.Google Scholar
  263. Wilson, K. G.: 1965, ‘Model Hamiltonians for Local Quantum Field Theory’,Phys. Rev. 140, 445–57.Google Scholar
  264. Wilson, K. G.: 1969, ‘Non-Lagrangian Models of Current Algebra’,Phys. Rev. 179, 1499–1512.Google Scholar
  265. Wilson, K. G.: 1970a, ‘Operator-Product Expansions and Anomalous Dimensions in the Thirring Model’,Phys. Rev. D2, 1473–77.Google Scholar
  266. Wilson, K. G.: 1970b, ‘Anomalous Dimensions and the Breakdown of Scale Invariance in Perturbation Theory’,Phys. Rev. D2, 1478–93.Google Scholar
  267. Wilson, K. G.: 1971, ‘Renormalization Group and Strong Interactions’,Phys. Rev. D3, 1818–46.Google Scholar
  268. Wilson, K. G.: 1975, ‘The Renormalization Group: Critical Phenomena and the Kondo Problem’,Rev. Mod. Phys. 47, 773–840.Google Scholar
  269. Wilson, K. G.: 1983, ‘The Renormalization Group and Critical Phenomena’,Rev. Mod. Phys. 55, 583–600.Google Scholar
  270. Wilson, K. G., and M. E. Fisher: 1972, ‘Critical Exponents in 3.99 Dimensions’,Phys. Rev. Lett. 28, 240–43.Google Scholar
  271. Wilson, K. G., and J. Kogut: 1974, ‘The Renomalization Group and the ε Expansion’,Physics Reports C12, 131–264.Google Scholar
  272. Wittgenstein, L.: 1922,Tractatus Logico-Philosophicus, ed. C. K. Ogden, Routledge and Kegan Paul, London.Google Scholar
  273. Wittgenstein, L.: 1953,Philosophical Investigations, ed. G. E. M. Anscombe, MacMillan, London.Google Scholar
  274. Yang, C. N., and R. L. Mills: 1954a, ‘Isotopic Spin Conservation and a Generalized Gauge Invariance’,Phys. Rev. 95, 631.Google Scholar
  275. Yang, C. N., and R. L. Mills: 1954b, ‘Conservation of Isotopic Spin and Isotopic Gauge Invariance’,Phys. Rev. 96, 191–95.Google Scholar

Copyright information

© Kluwer Academic Publishers 1993

Authors and Affiliations

  • Tian Yu Cao
    • 1
    • 2
  • Silvan S. Schweber
    • 1
    • 2
  1. 1.Department of PhysicsBrandeis UniversityWalthamUSA
  2. 2.Department of the History of ScienceHarvard UniversityCambridgeUSA

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