Hostname: page-component-78c5997874-8bhkd Total loading time: 0 Render date: 2024-11-06T12:06:33.218Z Has data issue: false hasContentIssue false
  • English
  • Français

On the Brout–Englert–Higgs–Guralnik–Hagen–Kibble Mechanism in Quantum Gravity

Published online by Cambridge University Press:  24 January 2018

Gerard ‘t Hooft
Gerard ‘t Hooft*
Affiliation:
Institute for Subatomic Physics, Centre for Extreme Matter and Emergent Phenomena (EMMEΦ), Utrecht University, Princetonplein 5, 3584 CC Utrecht, the Netherlands. Email: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

Local gauge invariance can materialise in different ways in theories for quantised elementary particles. It is less well-known, however, that a quite similar situation also occurs in the Einstein–Hilbert formalism for the gravitational forces. This may have important consequences for quantum theory. At first sight one may even think that it renders gravity renormalisable, just as happens in local gauge theories, but in gravity the truth is more puzzling.

Type
Tribute to Thomas W.B. Kibble
Information
European Review , Volume 26 , Issue 1 , February 2018 , pp. 110 - 116
Copyright
© Academia Europæa 2018 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1. Yang, C.N. and Mills, R.L. (1954) Conservation of isotopic spin and isotopic gauge invariance. Physical Review, 96, p. 191. doi: 10.1103/PhysRev96.191.Google Scholar
2. Shaw, R. (1955) The problem of particle types and other contributions to the theory of elementary particles. PhD thesis, University of Cambridge (unpublished).Google Scholar
3. Nambu, Y. (1960) Quasi-particles and gauge invariance in the theory of superconductivity. Physical Review, 117, p. 648. doi: 10.1103/PhysRev.117.648.Google Scholar
4. Goldstone, J. (1961) Field theories with ‘superconductor’ solutions. Nuovo Cimento, 19, p. 154. doi: 10.1007/BF02812722.CrossRefGoogle Scholar
5. Higgs, P.W. (1964) Broken symmetries, massless particles and gauge fields. Physics Letters, 12, p. 132. doi: 10.1016/0031-9163(64)91136-9.Google Scholar
6. Higgs, P.W. (1964) Broken symmetries and the masses of gauge bosons. Physical Review Letters, 13, p. 508. doi: 10.1103/PhysRevLett.13.508.CrossRefGoogle Scholar
7. Englert, F. and Brout, R. (1964) Broken symmetry and the mass of gauge vector mesons. Physical Review Letters, 13, p. 321. doi: 10.1103/PhysRevLett.13.321.Google Scholar
8. Guralnik, G.S., Hagen, C.R. and Kibble, T.W.B. (1964) Global conservation laws and massless particles. Physical Review Letters, 13, p. 585. doi: 10.1103/PhysRevLett.13.585.CrossRefGoogle Scholar
9. Anderson, P.W. (1963) Plasmons, gauge invariance, and mass. Physical Review, 130, p. 439. doi: 10.1103/PhysRev.130.439.Google Scholar
10. Faddeev, L. (2002) Mass in quantum Yang–Mills theory (comment on a Clay millennium problem). Bulletin of the Brazilian Mathematical Society, New Series, 33, 201. doi: 10.1007/s005740200009.CrossRefGoogle Scholar
11. ‘t Hooft, G. (2015) New physics is needed to understand black holes, or renormalization of the gravitational force in analogy with the electroweak theory. Lectures at the Erice International School of Subnuclear Physics, 26–27 June 2015 (unpublished).Google Scholar
12. ‘t Hooft, G. (2017) Local conformal symmetry in black holes, standard model, and quantum gravity. International Journal of Modern Physics D, 26, p. 1730006. doi: 10.1142/S0218271817300063.Google Scholar
13. Mannheim, P.D. (2012) Making the case for conformal gravity. Foundations of Physics, 42, p. 388. doi: 10.1007/s10701-011-9608-6.Google Scholar
14. Mannheim, P.D. (2016) Extension of the CPT theorem to non-Hermitian Hamiltonians and unstable states. Physics Letters B, 753, p. 288. doi: 10.1016/j.physletb.2015.12.033.Google Scholar
15. Lee, T.D. and Wick, G.C. (1969) Negative metric and the unitarity of the S-matrix. Nuclear Physics B, 9, p. 209. doi: 10.1016/0550-3213(69)90098-4.Google Scholar
16. ‘t Hooft, G. (2016) The firewall transformation for black holes and some of its implications. Foundations of Physics, 47, p. 1503. doi: 10.1007/s10701-017-0122-3.CrossRefGoogle Scholar