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The quantum theory of gravitation, effective field theories, and strings: yesterday and today

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Abstract

This paper analyzes the effective field theory perspective on modern physics through the lens of the quantum theory of gravitational interaction. The historical part argues that the search for a theory of quantum gravity stimulated the change in outlook that characterizes the modern approach to the standard model of particle physics and general relativity. We present some landmarks covering a long period, i.e., from the beginning of the 1930s until 1994, when, according to Steven Weinberg, the modern bottom–up approach to general relativity began. Starting from the first attempt to apply the quantum field theory techniques to quantize Einstein’s theory perturbatively, we explore its developments and interaction with the top–down approach encoded by string theory. In the last part of the paper, we focus on this last approach to describe the relationship between our modern understanding of string theory and effective field theory in today’s panorama. To this end, the non-historical part briefly explains the modern concepts of moduli stabilization and Swampland to understand another change in focus that explains the present framework where some string theorists move.

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Notes

  1. Their analysis stimulated the discussion about the contraposition between reductionism and anti-reductionism points of view.

  2. As we specify in the following, the QG research played an important role in understanding how to quantize non-abelian field theories.

  3. Rosenfeld would become an opponent to the idea of a quantized gravitational interaction only after the end of the 1950s.

  4. The graviton would be identified with a spin-two particle in the following years by Paul Fierz and Wolfgang Pauli [67].

  5. Besides Schwinger’s techniques, in those years, Richard Feynman’s, Ichiro Tomonaga’s, and Freeman Dyson’s contributions also emerged. Schwinger was invited to the Solvay conference but cannot attend the meeting.

  6. At the lowest order in perturbation theory, the electromagnetic ghosts decouple entirely, and the gravitational ghosts are not needed in the one-graviton exchange graphs considered by DeWitt.

  7. The discussions between Feynman and DeWitt stimulated DeWitt’s development of the quantization of both GR and non-Abelian gauge theories. The latter are the building blocks of the SM, which describes the non-gravitational fundamental interactions, i.e., the electroweak and the strong forces.

  8. The situation is different from QED, where only terms occur with a form already present in the Maxwell Lagrangian

  9. Fock discussed Bronstein’s PhD’s work.

  10. For more on this, see [10]. Other historical material can be found on the website http://theor.jinr.ru/ of the Bogoliubov Laboratory of Theoretical Physics. The Memorial Web Pages contain a description of Ogievetsky’s scientific work and some recollections of his colleagues.

  11. See also [42, p. 710].

  12. Salam had already written the papers that would earn him the Nobel Prize 10 years later.

  13. According to Duff, the motivation already appeared in an internal ICTP report dated 1973 [35, p. 2].

  14. Sardelis performed an analysis similar to Duff’s work for the Reissner–Nordström solution, which describes the space-time metric of a charged massive particle in GR.

  15. The covariant approach is the research program initiated by Rosenfeld and developed by Gupta and Feynman.

  16. He explicitly declared to ignore the possibility of a cosmological constant.

  17. For more details, see [16, 82].

  18. At the time, Weyl hoped that his Ansatz could “imply the existence of the electron and other unexplained atomic phenomena” [101] [102, p. 34].

  19. The two authors did not quote Feynman’s and DeWitt’s contributions we described in Sect.  2.4.

  20. Sakharov was awarded the Nobel Peace Prize in 1975 “for his struggle for human rights in the Soviet Union, for disarmament and cooperation between all nations” (www.nobelprize.org).

  21. In his analysis of the origin of the EFT approach in the work of Kenneth Wilson, Rivat pointed out that Sakharov’s paper “would deserve special scrutiny” [71, p. 321]

  22. Georgi’s work started before the birth of Quantum Chromodynamics.

  23. According to the authors: “we conjecture that the ghost difficulty could be avoided and the unitarity restored if the parameters of the theory approach a UV (necessarily non-Gaussian) fixed point [...] Of course it is not easy to calculate non-Gaussian fixed points” [57, p. 151].

  24. Donoghue was referring to [38], where Jürg Gasser and Heinrich Leutwyler systematized the combined use of phenomenological Lagrangians and symmetry to investigate chiral physics “including all of the low energy operators and performing the full renormalization at one loop” [32].

  25. Adler presented his point of view at the second Shelter Island conference, as described in Schweber [83].

  26. Superstring theory incorporates supersymmetry, which permits the inclusion of fermionic particles in the spectrum of the theory to obtain a theory of everything.

  27. See also Sect. 4 for further comments connected with the present status of research in ST.

  28. How ST incorporates Einstein’s theory is discussed in Sect.  4.

  29. The nonperturbative pseudo-solutions, which produce the so-called ghosts, are the source of the sicknesses of higher derivative theories.

  30. This event is sometimes called first string revolution.

  31. Iwasaki’s work was known to Gupta and his collaborator Stanley Radford who investigated the gravitational two-particle potential at the end of 1970s to clarify how it can be derived from the scattering operator by using the techniques of the standard QFT.

  32. This principle states that theories of science that are applicable in vastly different length scales can be sufficiently independent from each other such that lack of knowledge of the more microscopic theories does not forbid progress of the theories at larger length scales. In other words, chemistry can be done without solving the puzzles of the Standard Model of Particle Physics. The decoupling theorem dates back to 1975 with the work of Thomas Appelquist and James Carazzone [4].

  33. Follow the link to the recorded lectures on https://www.mpiwg-berlin.mpg.de/event/history-physics.

References

  1. Adler, S.L. 1982. Einstein Gravity as a Symmetry-Breaking Effect in Quantum Field Theory. Reviews of Modern Physics 54: 729 .

    Article  ADS  MathSciNet  Google Scholar 

  2. Adler, S.L. 1983, 5. EINSTEIN GRAVITATION AS A LONG WAVELENGTH EFFECTIVE FIELD THEORY. In Shelter Island II, pp. 162.

  3. Amati, D., M. Ciafaloni, and G. Veneziano. 1987. Superstring Collisions at Planckian Energies. Physics Letters B 197: 81 .

    Article  ADS  Google Scholar 

  4. Appelquist, T. and J. Carazzone. 1975. Infrared singularities and massive fields. Phys. Rev. D 11: 2856–2861 .

    Article  ADS  Google Scholar 

  5. Arkani-Hamed, N., L. Motl, A. Nicolis, and C. Vafa. 2007. The string landscape, black holes and gravity as the weakest force. JHEP 06: 060 .

    Article  ADS  MathSciNet  Google Scholar 

  6. Berends, F.A. and R. Gastmans. 1975a. On the High-Energy Behavior in Quantum Gravity. Nuclear Physics B 88: 99–108 .

    Article  ADS  Google Scholar 

  7. Berends, F.A. and R. Gastmans. 1975b. Quantum Gravity and the electron and Muon Anomalous Magnetic Moments. Physics Letters B 55: 311–312 .

    Article  ADS  Google Scholar 

  8. Berends, F.A. and R. Gastmans. 1976. Quantum Electrodynamical Corrections to Graviton-Matter Vertices. Annals of Physics 98: 225 .

    Article  ADS  Google Scholar 

  9. Bousso, R. and J. Polchinski. 2000. Quantization of four form fluxes and dynamical neutralization of the cosmological constant. JHEP 06: 006. https://doi.org/10.1088/1126-6708/2000/06/006. arxiv:hep-th/0004134

  10. Brian Pitts, J. 2012. The nontriviality of trivial general covariance: How electrons restrict ‘time’ coordinates, spinors (almost) fit into tensor calculus, and 716 of a tetrad is surplus structure. Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 43: 1–24 .

    Article  ADS  MathSciNet  Google Scholar 

  11. Bronstein, M.P. 1936. Quantentheorie schwacher gravitationsfelder. Physikalische Zeitschrift der Sowjetunion 9: 140–157 .

    Google Scholar 

  12. Bronstein, M.P. 2012. Republication of: Quantum theory of weak gravitational fields. General Relativity and Gravitation 44: 267–283 .

    Article  ADS  MathSciNet  Google Scholar 

  13. Cao, T.Y. and S. Schweber. 1993. The conceptual foundations and the philosophical aspects of renormalization theory. Synthese 97: 33–108 .

    Article  MathSciNet  Google Scholar 

  14. Castellani, E. 2002. Reductionism, emergence, and effective field theories. Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 33(2): 251–267 .

    Article  ADS  MathSciNet  Google Scholar 

  15. Chris J. Isham, R.P. and D.W. Sciama eds. 1975. Quantum Gravity. An Oxford Symposium, Oxford. Clarendon Press.

  16. Clifton, T., P.G. Ferreira, A. Padilla, and C. Skordis. 2012. Modified gravity and cosmology. Physics Reports 513: 1–189 .

    Article  ADS  MathSciNet  Google Scholar 

  17. Danielsson, U.H. and T. Van Riet. 2018. What if string theory has no de Sitter vacua? Int. J. Mod. Phys. D 27(12): 1830007. arXiv:1804.01120 [hep-th].

    Article  ADS  MathSciNet  Google Scholar 

  18. de Alwis, S.P. 1986. Strings in Background Fields, Beta Functions and Vertex Operators. Physical Review D 34: 3760. https://doi.org/10.1103/PhysRevD.34.3760.

    Article  ADS  MathSciNet  Google Scholar 

  19. Delbourgo, R. and P. Phocas-Cosmetatos. 1972. Radiative corrections to the electron graviton vertex. Lettere al Nuovo Cimento 5: 420–422 .

    Article  Google Scholar 

  20. Delbourgo, R. and A. Salam. 1972. The gravitational correction to pcac. Physics Letters B 40: 381–382 .

    Article  ADS  Google Scholar 

  21. Delbourgo, R., A. Salam, and J.A. Strathdee 1969a, 4. Infinities in Einstein’s gravitational theory. IC-69-28.

  22. Delbourgo, R., A. Salam, and J.A. Strathdee. 1969b. Suppression of infinities in einstein’s gravitational theory. Lettere al Nuovo Cimento 2S1: 354–359 .

  23. Deser, S.D., M.T. Grisaru, and H. Pendleton eds. 1970. Proceedings, 13th Brandeis University Summer Institute in Theoretical Physics, Lectures On Elementary Particles and Quantum Field Theory: Waltham, MA, USA, June 15 - July 24 1970, Cambridge, MA, USA. MIT.

    Google Scholar 

  24. DeWitt, B.S. 1986. Effective action for expectation values, In Quantum Concepts in Space and Time, eds. Penrose, R. and C. Isham, 325–336. Oxford: Clarendon Press.

    Google Scholar 

  25. DeWitt-Morette, C. 2011. The Pursuit of Quantum Gravity: Memoirs of Bryce DeWitt from 1946 to 2004. Berlin: Springer.

    Book  Google Scholar 

  26. DeWitt (Seligman), C.B. 1949, December. On the theory of gravitational interactions, and the interaction of gravitation with light. Harvard University Archives Pusey Library Cambridge, MA 02138.

  27. Dicke, R.H. and H.M. Goldenberg. 1967. Solar oblateness and general relativity. Physical Review Letters 18: 313–316 .

    Article  ADS  Google Scholar 

  28. Dine, M. and N. Seiberg. 1985. Is the Superstring Weakly Coupled? Phys. Lett. B 162: 299–302. https://doi.org/10.1016/0370-2693(85)90927-X.

    Article  ADS  MathSciNet  Google Scholar 

  29. Dirac, P.A.M. 1932. Relativistic quantum mechanics. Proceedings of the Royal Society of London A 136: 453–464 .

    ADS  Google Scholar 

  30. Donoghue, J.F. 1994a. General relativity as an effective field theory: The leading quantum corrections. Phys. Rev. D 50: 3874–3888 .

    Article  ADS  Google Scholar 

  31. Donoghue, J.F. 1994b. Leading quantum correction to the Newtonian potential. Phys. Rev. Lett. 72: 2996–2999 .

    Article  ADS  Google Scholar 

  32. Donoghue, J.F. 2022. Private Communication.

  33. Duff, M.J. 1973. Quantum Tree Graphs and the Schwarzschild Solution. Physical Review D 7: 2317–2326 .

    Article  ADS  Google Scholar 

  34. Duff, M.J. 1974. Quantum corrections to the Schwarzschild solution. Physical Review D 9: 1837–1839 .

    Article  ADS  Google Scholar 

  35. Duff, M.J. 2021. Chris Isham: mentor, colleague, friend. arXiv:2112.13722 [physics.hist-ph].

  36. Dunne, G.V. 2012. THE HEISENBERG–EULER EFFECTIVE ACTION: 75 YEARS ON, Volume 27, pp. 1260004:1–16. World Scientific Press.

  37. Fock, V.A. ed. 1968. 5th International Conference on Gravity and the Theory of Relativity held at Tbilisi, Sept. 9–16, 1968., Tbilisi. Publishing House of Tbilisi University.

  38. Gasser, J. and H. Leutwyler. 1984. Chiral Perturbation Theory to One Loop. Annals of Physics 158: 142 .

    Article  ADS  MathSciNet  Google Scholar 

  39. Gava, E., R. Iengo, and C.J. Zhu. 1989. Quantum Gravity Corrections From Superstring Theory. Nuclear Physics B 323: 585–613 .

    Article  ADS  MathSciNet  Google Scholar 

  40. Georgi, H. 1989. Grand unified theories, In The New Physics, ed. Davies, P., 425–445. Cambridge, UK: Cambridge University Press.

    Google Scholar 

  41. Georgi, H., H.R. Quinn, and S. Weinberg. 1974. Hierarchy of Interactions in Unified Gauge Theories. Physical Review Letters 33: 451–454 .

    Article  ADS  Google Scholar 

  42. Goroff, M.H. and A. Sagnotti. 1986. The Ultraviolet Behavior of Einstein Gravity. Nuclear Physics B 266: 709–736 .

    Article  ADS  Google Scholar 

  43. Green, M.B. and J.H. Schwarz. 1984. Anomaly Cancellation in Supersymmetric D=10 Gauge Theory and Superstring Theory. Physics Letters B 149: 117–122 .

    Article  ADS  MathSciNet  Google Scholar 

  44. Gupta, S.N. 1952a. quantization of einstein’s gravitational field: Linear approximation. Proceedings of the Physical Society. Section A 65: 161–169 .

  45. Gupta, S.N. 1952b. quantization of einstein’s gravitational field: general treatment. Proceedings of the Physical Society. Section A 65: 608–619 .

  46. Gupta, S.N. 1954. Gravitation and Electromagnetism. Physical Review 96: 1683–1685 .

    Google Scholar 

  47. Halpern, L. 1962. On the role of gravitational fields in some elementary particle processes. Il Nuovo Cimento 25: 1239–1269 .

    Article  ADS  MathSciNet  Google Scholar 

  48. Hartmann, S. 2001, 01. Effective field theories, reduction and scientific explanation. Studies in History and Philosophy of Modern Physics 31: 70–90 .

    Google Scholar 

  49. Hiida, K. and M. Kikugawa. 1971. Quantum theory of gravity and the perihelion motion of the mercury. Progress in Theoretical Physics 46: 1610–1622 .

    Article  ADS  Google Scholar 

  50. Hossenfelder, S. 2018. Lost in math: How beauty leads physics astray. New York: Basic Books.

    Google Scholar 

  51. Iengo, R. and K. Lechner. 1990. Schwarzschild Like Corrections to Gravity From Superstrings at One Loop. Nuclear Physics B 335: 221–244 .

    Article  ADS  Google Scholar 

  52. Infeld, L. ed. 1962. Relativistic Theories of Gravitation, OXFORD - LONDON - EDINBURGH - NEW YORK PARIS - FRANKFURT. PERGAMON PRESS.

    Google Scholar 

  53. Iwanenko, D.D. 1967. Fifty years of soviet work on gravitation. Soviet Physics Journal 10(10): 30–38 .

    Google Scholar 

  54. Iwanenko, D.D. 1970. The problems of unifying cosmology with microphyscs, In Physics, Logic and History. Based on the first International Colloqium held at the University of Denver, May 16-20, 1966, eds. Yourgrau, W. and A.D. Breck, 105–114. New Your - London: Plenum Press.

    Google Scholar 

  55. Iwasaki, Y. 1971. Quantum theory of gravitation vs. classical theory. - fourth-order potential. Prog. Theor. Phys. 46: 1587–1609. https://doi.org/10.1143/PTP.46.1587.

    Article  ADS  Google Scholar 

  56. Jacobsen, A.S. 2012. Léon Rosenfeld: physics, philosophy, and politics in the twentieth century. Singapore, London: World scientific.

    Book  Google Scholar 

  57. Julve, J. and M. Tonin. 1978. Quantum Gravity with Higher Derivative Terms. Nuovo Cimento B 46: 137–152 .

    Article  ADS  MathSciNet  Google Scholar 

  58. Lawrence, J.K. 1971. Gravitational fermion interactions. General Relativity and Gravitation 2: 215–222 .

    Article  ADS  Google Scholar 

  59. Lechner, K. 1990. Four graviton scattering in \(D = 4\) superstrings with broken space-time supersymmetry. Nuclear Physics B 345: 248–280.

  60. Lechner, K. 2022. Private Communication.

  61. Lüst, D., E. Palti, and C. Vafa. 2019. AdS and the Swampland. Phys. Lett. B 797: 134867. https://doi.org/10.1016/j.physletb.2019.134867. arXiv:1906.05225 [hep-th].

    Article  MathSciNet  Google Scholar 

  62. Martinez, J.P. 2019. Soviet Science as Cultural Diplomacy during the Tbilisi Conference on General Relativity. Vestnik of Saint Petersburg University. History 64: 120–135 .

  63. Montero, M., C. Vafa, and I. Valenzuela. 2023. The dark dimension and the swampland. JHEP 02: 022. arXiv:2205.12293 [hep-th].

    Article  ADS  MathSciNet  Google Scholar 

  64. Nepomechie, R. 1984. Einstein gravity as the low energy effective theory of weyl gravity. Physics Letters B 136(1): 33–37 .

    Article  ADS  MathSciNet  Google Scholar 

  65. Ogievetsky, V. and I. Polubarinov. 1965. Interacting field of spin 2 and the einstein equations. Annals of Physics 35(2): 167–208 .

    Article  ADS  Google Scholar 

  66. Ooguri, H., E. Palti, G. Shiu, and C. Vafa. 2019. Distance and de Sitter Conjectures on the Swampland. Phys. Lett. B 788: 180–184. https://doi.org/10.1016/j.physletb.2018.11.018. arXiv:1810.05506 [hep-th].

    Article  ADS  MathSciNet  Google Scholar 

  67. Pauli, W. and M. Fierz. 1939. Über relativistische feldgleichungen von teilchen mit beliebigem spin im elektromagnetischen feld. Helvetica Physica Acta 12: 297–300 .

    ADS  Google Scholar 

  68. Pechlaner, E. and R. Sexl. 1966. On quadratic lagrangians in General Relativity. Communications in Mathematical Physics 2(1): 165–175 .

    Article  ADS  MathSciNet  Google Scholar 

  69. Rickles, D. 2014. A Brief History of String Theory. From Dual Models to M-Theory. Berlin Heidelberg: Springer-Verlag.

    Book  Google Scholar 

  70. Rickles, D. 2020. Covered with Deep Mist: The Development of Quantum Gravity (1916-1956). Oxford: Oxford University Press.

    Book  Google Scholar 

  71. Rivat, S. 2021. Drawing scales apart: The origins of wilson’s conception of effective field theories. Studies in History and Philosophy of Science Part A 90: 321–338 .

    Article  MathSciNet  Google Scholar 

  72. Rivat, S. and A. Grinbaum. 2020. Philosophical foundations of effective field theories. The European Physical Journal A 56: 90 .

    Article  ADS  Google Scholar 

  73. Rosenfeld, L. 1930. Über die Gravitationwirkungen des Lichtes. Zeitschrift für Physik 65: 589–599 .

    Article  ADS  Google Scholar 

  74. Rovelli, C. 2000. Notes for a brief history of quantum gravity. In 9th Marcel Grossmann Meeting on Recent Developments in Theoretical and Experimental General Relativity, Gravitation and Relativistic Field Theories (MG 9), pp. 742–768.

  75. Sakharov, A. 1990. Memoirs. New York: Alfred A. Knopf. Translated from the Russian by Richard Lourik.

    Google Scholar 

  76. Sakharov, A.D. 1967. Vakuumnye kvantovye fluktuacii v iskrivlennom prostranstve i teoria gravitacii. Doklady Akademii Nauk SSSR Ser. Fiz. 177: 70–71 .

    ADS  Google Scholar 

  77. Sakharov, A.D. 2000. Vacuum quantum fluctuations in curved space and the theory of gravitation. General Relativity and Gravitation 32: 365–367 .

    Article  ADS  MathSciNet  Google Scholar 

  78. Salam, A. 1992. Gauge unification of fundamental forces, In Nobel Lectures. Physics 1971–1980, ed. Lundqvist, S., 513–538. Princeton (New Jersey): World Scientific Press.

    Google Scholar 

  79. Sardelis, D.A. 1973. QUANTUM GRAVITY AND REISSNER-NORDSTROM SOLUTION. PhD Thesis - Imperial College of Science and Technology.

  80. Sardelis, D.A. 1975a. Minimum size of charged particles in general relativity. General Relativity and Gravitation 6: 409–422 .

    Article  ADS  MathSciNet  Google Scholar 

  81. Sardelis, D.A. 1975b. The tree graphs of quantum gravity and the Reissner-Nordstrm̈ solution. General Relativity and Gravitation 6: 551–565 .

    Article  ADS  MathSciNet  Google Scholar 

  82. Schmidt, H.J. 2007. Fourth order gravity: Equations, history, and applications to cosmology. International Journal of Geometric Methods in Modern Physics 04(02): 209–248 .

    Article  MathSciNet  Google Scholar 

  83. Schweber, S. 2016. The shelter island conferences revisited: “fundamental” physics in the decade 1975–1985. Physics in Perspective 18: 58–147 .

    Article  ADS  Google Scholar 

  84. Simon, J.Z. 1991. The Stability of flat space, semiclassical gravity, and higher derivatives. Physical Review D 43: 3308–3316 .

    Article  ADS  MathSciNet  Google Scholar 

  85. Smolin, L. 2006. The trouble with physics: The rise of string theory, the fall of a science, and what comes next.

  86. Stelle, K.S. 1977. Renormalization of Higher Derivative Quantum Gravity. Physical Review D 16: 953–969 .

    Article  ADS  MathSciNet  Google Scholar 

  87. Stelle, K.S. 1978. Classical Gravity with Higher Derivatives. General Relativity and Gravitation 9: 353–371 .

    Article  ADS  MathSciNet  Google Scholar 

  88. Stoops, R. ed. 1950. Les particules élémentaires: huitième Conseil de physique, tenu à l’Université de Bruxelles du 27 septembre au 2 octobre 1948., Bruxelles. Institut international de physique Solvay.

    Google Scholar 

  89. Susskind, L. 2007. The anthropic landscape of string theory, pp. 247–266. Cambridge University Press.

  90. ’t Hooft, G. and M.J.G. Veltman. 1974. One loop divergencies in the theory of gravitation. Annales de l’Institut Henri Poincaré, physique théorique A 20: 69–94 .

  91. Utiyama, R. and B.S. DeWitt. 1962. Renormalization of a classical gravitational field interacting with quantized matter fields. Journal of Mathematics and Physics 3: 608–618 .

    Article  MathSciNet  Google Scholar 

  92. Vafa, C. 2005, 9. The String landscape and the swampland. arXiv:hep-th/0509212.

  93. Weinberg, S. 1965. Photons and gravitons in perturbation theory: Derivation of Maxwell’s and Einstein’s equations. Phys. Rev. 138: B988–B1002 .

    Article  ADS  MathSciNet  Google Scholar 

  94. Weinberg, S. 1976, 8. Critical Phenomena for Field Theorists. In 14th International School of Subnuclear Physics: Understanding the Fundamental Constitutents of Matter.

  95. Weinberg, S. 1979. Phenomenological Lagrangians. Physica A 96(1-2): 327–340 .

    Article  ADS  Google Scholar 

  96. Weinberg, S. 1980a. ultraviolet divergences in quantum theories of gravitation, In General Relativity: An Einstein Centenary Survey, eds. Hawking, S. and W. Israel, 790–831. Cambridge, UK: Cambridge University Press.

    Google Scholar 

  97. Weinberg, S. 1980b. conceptual foundations of the unified theory of weak and electromagnetic interactions. Reviews of Modern Physics 52: 515–523 .

    Article  ADS  MathSciNet  Google Scholar 

  98. Weinberg, S. 1995, 6. The Quantum theory of fields. Vol. 1: Foundations. Cambridge University Press.

  99. Weinberg, S. 2009. Effective Field Theory, Past and Future. Proceeding of Science CD09: 001 .

    Google Scholar 

  100. Weinberg, S. 2021. On the Development of Effective Field Theory. European Physics Journal H 46(1): 6 .

    Article  ADS  Google Scholar 

  101. Weyl, H. 1918. Gravitation und elektrizität. Sitzungsberichte der Königlich Preußischen Akademie der Wissenschaften 3: 465–480 .

    Google Scholar 

  102. Weyl, H. 1997. Gravitation and electricity, In The dawning of gauge theories, ed. O’Raifeartaigh, L., 24–37. Princeton (New Jersey): Princeton University Press.

    Google Scholar 

  103. Woit, P. 2006. Not even wrong: The Failure of String Theory & the Continuing Challenge to Unify the Laws of Physics.

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Acknowledgements

The authors thank John Donoghue and Kurt Lechner for sharing their reminiscences and the three anonymous referees for helping improve the original manuscript. A.R. is also grateful to Lechner for the discussions that helped clarify some mathematical details and to Ksenia Dobriakova for an Italian translation of Sakharov’s work.

Author information

Authors and Affiliations

  1. Theoretische Natuurkunde and Applied Physics Research Group (APHY), Vrije Universiteit Brussels (VUB) and Solvay Institutes, Pleinlaan 2, 1050, Brussels, Belgium

    Alessio Rocci

  2. Department of Physics and Astronomy, KU Leuven, Celestijnenlaan 200d, Box 2415, 3001, Leuven, Belgium

    Thomas Van Riet

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Correspondence to Alessio Rocci.

Appendix: Chronologies

Appendix: Chronologies

This appendix contains the events analyzed in the paper in chronological order. We did not create a unique timeline. We decided to keep the different sections separate for clarity.

1.1 The roots of the modern EFT of quantum GR

1.1.1 The analogy between electrodynamics and gravity

  1. 1930

    Rosenfeld applies the perturbative methods to quantum GR

  2. 1936

    Bronstein obtains the Newton potential as a one-graviton exchange

  3. 1948

    Solvay Physics Council: Oppenheimer comments on Rosenfeld’s work

1.1.2 Jablonna’s conference

  1. 1950

    DeWitt’s unpublished Ph.D. thesis.

  2. 1952

    Gupta reperforms and publishes DeWitt’s calculation.

  3. 1955

    Feynman starts his investigations on quantum GR

  4. 1962

    DeWitt and Utiyama’s paper shows the emergence of higher derivative terms in the context of quantum GR following Feynman’s unpublished investigations

  5. 1962

    Jablonna Conference. Ghosts and higher derivative terms are discussed. DeWitt suggests investigating the radiative corrections to Schwarzshild solution

1.1.3 The first quantum corrections to Newton’s potential

  1. 1962

    Halpern reintroduces gravitational interaction in scattering processes

  2. 1965

    Weinberg, Ogievetsky, and Polubarinov discuss the nonlinear effects of the spin-two field.

  3. 1969

    Delbourgo started his investigations on quantum GR

  4. 1971

    Iwasaki’s bottom–up approach to Mercury’s perihelion

  5. 1973

    Duff applies new renormalization techniques to Schwarzschild’s solution

  6. 1973

    Sardelis follows Duff and investigates Reissner-Nordström solution

  7. 1973

    “Quantum Gravity. An Oxford Symposium”

  8. 1974

    Duff calculates the quantum corrections to Newton’s potential by analyzing Schwarzschild’s solution

  9. 1974

    ’t Hooft and Veltman prove non-finiteness of quantum GR coupled with matter at one loop

  10. 1975

    Berends and Gastman investigate quantum gravity corrections at the one-loop level to the electron and muon (g-2)/2

  11. 1986

    Goroff and Sagnotti prove non-finiteness of pure quantum GR at the two-loop level

1.1.4 The role of higher derivative theories

  1. 1918

    Weyl publishes his higher derivative theory for gravity without the EH term

  2. 1935

    Euler and Kochel introduce the effective theory approach to deal with nonlinearities in QED

  3. 1936

    Euler and Heisenberg develop Euler and Kochel’s work

  4. 1947

    Gregory reintroduces the EH term in higher derivative theories

  5. 1954

    Schwinger introduces the concept of effective action

  6. 1966

    Pechlaner and Sechsel apply the concept of effective Lagrangian merging the frameworks of higher derivative theories and particle physics

  7. 1967

    Sakharov treats the EH term as the zeroth approximation of an effective quantum action

  8. 1975

    At Oxford’s symposium, Deser suggests the connection between nonrenormalizability and GR as an effective theory

  9. 1977

    Stelle discusses the renormalizability of higher derivative theories

1.2 Entering the modern era

  1. 1973

    Discovery of asymptotic freedom

  2. 1974

    Firsts models of Grand Unified Theories

  3. 1974

    Georgi, Quinn, and Weinberg discuss the running of coupling constants for strong, electroweak, and gravitational interaction

1.2.1 Weinberg’s role and the change in outlook

  1. 1962

    Jablonna Conference. Feynman points out the non-relevance of UV effects for the bottom–up approach

  2. 1975

    Oxford Symposium. Salam emphasizes the importance of the bottom–up approach, disregarding UV effects

  3. 1976

    Weinberg’s Erice lecture suggests a connection between asymptotic safety and difficulties in quantizing GR. Weinberg tarts challenging the renormalization criterion

  4. 1979

    Weinberg’s paper on EFT

  5. 1980

    In Einstein Centenary Survey, Weinberg uses the term “effective gravitational Lagrangian.” In his Nobel lecture, he introduces the EFT perspective

1.2.2 Toward the modern bottom–up approach

  1. 1970

    Zumino uses the massive EH action to describe spin 2 particles in the context of strong forces

  2. 1982

    Adler develops Sakharov’s work and discusses the gravitational effective action

  3. 1983

    Shelter Island II. Adler presents his EFT point of view

  4. 1984

    Nepomechie points out the analogy between strong and gravitational interactions from the EFT perspective

  5. 1987

    Goity shows that in the context of strong interaction, loop effects are independent of chiral parameters

1.2.3 Completing the puzzle: Strings versus QFT

  1. 1984

    Green and Schwarz publish the exaptation paper that marks the first string revolution

  2. 1986

    De Alwis uses Wilson’s renormalization techniques to show gravity and its higher derivative terms emerge as an effective action in String Theory

  3. 1991

    Simon discusses de Alwis’s result as a top–down perspective

  4. 1987

    Amati, Ciafaloni, and Veneziano develop the top–down strategy starting the investigation of infra-red effects

  5. 1990

    Iengo and Lechner analyze the classical and quantum one-loop corrections to the Newton potential, comparing top–down and bottom–up strategies

  6. 1993

    Donoghue performs his bottom–up calculation

  7. 1994

    Donoghue publishes the bottom–up classical and quantum one-loop corrections to Newton’s potential. He computes the coefficients and proposes a new research area that regularly applies EFT tools to quantum GR.

1.3 Strings and EFT: today

  1. 1975

    Appelquist and Carazzone publish the decoupling theorem

  2. 1985

    Dine and Seiberg formulate the so-called Dine-Seiberg problem

  3. 2000

    Bousso and Polchinski discuss the emerging Landscape scenario

  4. 2005

    To solve the problems connected with the Landscape, Vafa proposes a shift in focus and the Swampland scenario

  5. 2006

    Woit publishes his critics to String Theory in Not even wrong

  6. 2007

    Arkani-Hamed and his collaborators discuss the Weak Gravity Conjecture

  7. 2019

    Ooguri and his collaborators introduce the de Sitter conjecture; Lj̈ust and his collaborators discuss the AdS distance conjecture

  8. 2023

    Montero and his collaborators discuss the empirical consequences of the AdS distance conjecture

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Rocci, A., Van Riet, T. The quantum theory of gravitation, effective field theories, and strings: yesterday and today. EPJ H 49, 7 (2024). https://doi.org/10.1140/epjh/s13129-024-00069-4

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