Advertisement

Fakeons and the classicization of quantum gravity: the FLRW metric

  • Damiano AnselmiEmail author
Open Access
Regular Article - Theoretical Physics
  • 30 Downloads

Abstract

Under certain assumptions, it is possible to make sense of higher derivative theories by quantizing the unwanted degrees of freedom as fakeons, which are later projected away. Then the true classical limit is obtained by classicizing the quantum theory. Since quantum field theory is formulated perturbatively, the classicization is also perturbative. After deriving a number of properties in a general setting, we consider the theory of quantum gravity that emerges from the fakeon idea and study its classicization, focusing on the FLRW metric. We point out cases where the fakeon projection can be handled exactly, which include radiation, the vacuum energy density and the combination of the two, and cases where it cannot, which include dust. Generically, the classical limit shares many features with the quantum theory it comes from, including the impossibility to write down complete, “exact” field equations, to the extent that asymptotic series and nonperturbative effects come into play.

Keywords

Models of Quantum Gravity Classical Theories of Gravity Beyond Standard Model Cosmology of Theories beyond the SM 

Notes

Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.

References

  1. [1]
    D. Anselmi, On the quantum field theory of the gravitational interactions, JHEP 06 (2017) 086 [arXiv:1704.07728] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  2. [2]
    D. Anselmi, Fakeons And Lee-Wick Models, JHEP 02 (2018) 141 [arXiv:1801.00915] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  3. [3]
    D. Anselmi and M. Piva, The Ultraviolet Behavior of Quantum Gravity, JHEP 05 (2018) 027 [arXiv:1803.07777] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  4. [4]
    D. Anselmi and M. Piva, Quantum Gravity, Fakeons And Microcausality, JHEP 11 (2018) 021 [arXiv:1806.03605] [INSPIRE].ADSCrossRefzbMATHGoogle Scholar
  5. [5]
    D. Anselmi and M. Piva, A new formulation of Lee-Wick quantum field theory, JHEP 06 (2017) 066 [arXiv:1703.04584] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  6. [6]
    R.E. Cutkosky, Singularities and discontinuities of Feynman amplitudes, J. Math. Phys. 1 (1960) 429 [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  7. [7]
    M.J.G. Veltman, Unitarity and causality in a renormalizable field theory with unstable particles, Physica 29 (1963) 186 [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  8. [8]
    M.E. Peskin and D.V. Schroeder, An introduction to quantum field theory, Addison-Wesley, Reading, U.S.A, (1995), Chapter 7, section 3.Google Scholar
  9. [9]
    T.D. Lee and G.C. Wick, Negative Metric and the Unitarity of the S Matrix, Nucl. Phys. B 9 (1969) 209 [INSPIRE].
  10. [10]
    T.D. Lee and G.C. Wick, Finite Theory of Quantum Electrodynamics, Phys. Rev. D 2 (1970) 1033 [INSPIRE].
  11. [11]
    N. Nakanishi, Lorentz noninvariance of the complex-ghost relativistic field theory, Phys. Rev. D 3 (1971) 811 [INSPIRE].
  12. [12]
    R.E. Cutkosky, P.V. Landshoff, D.I. Olive and J.C. Polkinghorne, A non-analytic S matrix, Nucl. Phys. B 12 (1969) 281 [INSPIRE].
  13. [13]
    B. Grinstein, D. O’Connell and M.B. Wise, Causality as an emergent macroscopic phenomenon: The Lee-Wick O(N) model, Phys. Rev. D 79 (2009) 105019 [arXiv:0805.2156] [INSPIRE].
  14. [14]
    D. Anselmi, Fakeons, Microcausality And The Classical Limit Of Quantum Gravity, Class. Quant. Grav. 36 (2019) 065010 [arXiv:1809.05037] [INSPIRE].
  15. [15]
    K.S. Stelle, Renormalization of Higher Derivative Quantum Gravity, Phys. Rev. D 16 (1977) 953 [INSPIRE].
  16. [16]
    I.G. Avramidi and A.O. Barvinsky, Asymptotic freedom in higher derivative quantum gravity, Phys. Lett. 159B (1985) 269 [INSPIRE].ADSCrossRefGoogle Scholar
  17. [17]
    N. Ohta, R. Percacci and A.D. Pereira, Gauges and functional measures in quantum gravity II: Higher derivative gravity, Eur. Phys. J. C 77 (2017) 611 [arXiv:1610.07991] [INSPIRE].
  18. [18]
    A. Salvio and A. Strumia, Agravity, JHEP 06 (2014) 080 [arXiv:1403.4226] [INSPIRE].
  19. [19]
    A. Salvio and A. Strumia, Agravity up to infinite energy, Eur. Phys. J. C 78 (2018) 124 [arXiv:1705.03896] [INSPIRE].
  20. [20]
    D. Anselmi, The correspondence principle in quantum field theory and quantum gravity, PhilSci 15287, OSF preprints https://doi.org/10.31219/osf.io/d2nj7 Preprints 2018110213 hal-01900207.
  21. [21]
    M.B. Green, J.H. Schwarz and E. Witten, Superstring Theory I & II, Cambridge University Press, (1987).Google Scholar
  22. [22]
    J. Polchinski, String Theory I & II, Cambridge University Press, (1998).Google Scholar
  23. [23]
    K. Becker, M. Becker and J. Schwarz, String theory and M-theory: A modern introduction, Cambridge University Press, (2007).Google Scholar
  24. [24]
    R. Blumenhagen, D. Lust and S. Theisen, Basic Concepts of String Theory, Springer Verlag, (2012).Google Scholar
  25. [25]
    A. Ashtekar ed.: 100 years of relativity. Space-time structure: Einstein and beyond, World Scientific, (2005).Google Scholar
  26. [26]
    C. Rovelli, Quantum Gravity, Cambridge University Press, (2004).Google Scholar
  27. [27]
    T. Thiemann, Modern canonical quantum general relativity, Cambridge University Press, (2007).Google Scholar
  28. [28]
    J.M. Maldacena, The large N limit of superconformal field theories and supergravity, Int. J. Theor. Phys. 38 (1999) 1113 [hep-th/9711200] [INSPIRE].
  29. [29]
    S.S. Gubser, I.R. Klebanov and A.M. Polyakov, Gauge theory correlators from noncritical string theory, Phys. Lett. B 428 (1998) 105 [hep-th/9802109] [INSPIRE].
  30. [30]
    E. Witten, Anti-de Sitter space and holography, Adv. Theor. Math. Phys. 2 (1998) 253 [hep-th/9802150] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  31. [31]
    V.E. Hubeny, The AdS/CFT Correspondence, Class. Quant. Grav. 32 (2015) 124010 [arXiv:1501.00007] [INSPIRE].
  32. [32]
    H.W. Hamber, Quantum Gravity on the Lattice, Gen. Rel. Grav. 41 (2009) 817 [arXiv:0901.0964] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  33. [33]
    S. Weinberg, Ultraviolet divergences in quantum theories of gravitation, in An Einstein centenary survey, S. Hawking and W. Israel eds., Cambridge University Press, Cambridge (1979), p. 790.Google Scholar
  34. [34]
    O. Lauscher and M. Reuter, Ultraviolet fixed point and generalized flow equation of quantum gravity, Phys. Rev. D 65 (2002) 025013 [hep-th/0108040] [INSPIRE].
  35. [35]
    O. Lauscher and M. Reuter, Flow equation of quantum Einstein gravity in a higher derivative truncation, Phys. Rev. D 66 (2002) 025026 [hep-th/0205062] [INSPIRE].
  36. [36]
    K. Falls, C.R. King, D.F. Litim, K. Nikolakopoulos and C. Rahmede, Asymptotic safety of quantum gravity beyond Ricci scalars, Phys. Rev. D 97 (2018) 086006 [arXiv:1801.00162] [INSPIRE].
  37. [37]
    M.R. Douglas, The statistics of string/M theory vacua, JHEP 05 (2003) 046 [hep-th/0303194] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  38. [38]
    S. Ashok and M.R. Douglas, Counting flux vacua, JHEP 01 (2004) 060 [hep-th/0307049] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  39. [39]
    D. Anselmi, Properties Of The Classical Action Of Quantum Gravity, JHEP 05 (2013) 028 [arXiv:1302.7100] [INSPIRE].ADSMathSciNetCrossRefzbMATHGoogle Scholar
  40. [40]
    G. ’t Hooft and M. Veltman, An illuminating discussion on causality in quantum field theory can be found, in Diagrammar, Section 6.1, CERN-73-09.
  41. [41]
    N.N. Bogoliubov and D.V. Shirkov, Introduction to the theory of quantized fields, Interscience Publishers, New York, U.S.A., (1959).Google Scholar
  42. [42]
    A.D. Linde, Inflationary Cosmology, Lect. Notes Phys. 738 (2008) 1 [arXiv:0705.0164] [INSPIRE].

Copyright information

© The Author(s) 2019

Authors and Affiliations

  1. 1.Dipartimento di Fisica “Enrico Fermi”Università di Pisa and INFN, Sezione di PisaPisaItaly

Personalised recommendations