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The Conformal Constraint in Canonical Quantum Gravity · Around

2010

The Conformal Constraint in Canonical Quantum Gravity

Hooft, Gerard 't

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Perturbative canonical quantum gravity is considered, when coupled to a renormalizable model for matter fields.

It is proposed that the functional integral over the dilaton field should be disentangled from the other integrations over the metric fields.
This should generate a conformally invariant theory as an intermediate result, where the conformal anomalies must be constrained to cancel out.
When the residual metric is treated as a background, and if this background is taken to be flat, this leads to a novel constraint: in combination with the dilaton contributions, the matter lagrangian should have a vanishing beta function.

Built on

S.L. Adler, Phys. Rev. 177
1969
Earlier work this paper cites.
S.L. Adler and W.A. Bardeen, Phys. Rev
1969
Earlier work this paper cites.
D.R.T. Jones, Nucl. Phys. B75
1983
Earlier work this paper cites.

Similar

L. Brink, J.H. Schwarz and J. Scherk, Supersymmetric Yang-Mills Theories , ERDA Research and development report, CALT-68-574 (1976); M. Sohnius Introducing supersymmetry , Physics Reports 128
1985
Cited alongside, same era.
D.M. Capper and M.J. Duff, Conformal Anomalies and the Renormalizability Problem in Quantum Gravity
1993
Cited alongside, same era.
G. ’t Hooft, The birth of asymptotic freedom , Nucl. Phys. B254
2007
Cited alongside, same era.
G. ’t Hooft, Probing the small distance structure of canonical quantum gravity using the conformal group , arXiv:1009.0669v2 [gr-qc]
Original
Cited in the paper.
A.G.M. Pickering, J.A. Gracey and D.R.T. Jones, Three loop gauge beta-function for the most general single gauge-coupling theory , arXiv:hep-ph/0104247
Cited in the paper.

Then

C.M. Bender and P.D. Mannheim, No-ghost theorem for the fourth-order derivative Pais-Uhlenbeck oscillator model
Original
2008
Later among the works it cites.
G. ’t Hooft, Quantum Gravity without Space-time Singularities or Horizons , Erice School of Subnuclear Physics 2009, to be publ.; arXiv:0909.3426
Original
2009
Later among the works it cites.
P. D. Mannheim and D. Kazanas, Astrophys. J. 342
Original
2010
Closest in time.

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