%0 Journal Article %1 Hooft2010 %A Hooft, Gerard 't %D 2010 %K quantum spacetime %T Probing the small distance structure of canonical quantum gravity using the conformal group %U http://arxiv.org/abs/1009.0669 %X In canonical quantum gravity, the formal functional integral includes an integration over the local conformal factor, and we propose to perform the functional integral over this factor before doing any of the other functional integrals. By construction, the resulting effective theory would be expected to be conformally invariant and therefore finite. However, also the conformal integral itself diverges, and therefore the actual situation is more delicate. The effects of a renormalization counter term are considered, including the associated problem of unitarity violation, such as a Landau-like ghost. Adding (massive or massless) matter fields does not change the picture; to confirm this, detailed calculations were necessary, and they are presented. Some alternative ideas are offered, including a more daring speculation, which is that no counter term should be allowed for at all. This has far-reaching and important consequences, which we discuss. A surprising picture emerges of quantized elementary particles interacting with a gravitational field that is "partly classical". This approach was inspired by a search towards the reconciliation of Hawking radiation with unitarity and locality, and it offers basic new insights there.

@article{Hooft2010, abstract = { In canonical quantum gravity, the formal functional integral includes an integration over the local conformal factor, and we propose to perform the functional integral over this factor before doing any of the other functional integrals. By construction, the resulting effective theory would be expected to be conformally invariant and therefore finite. However, also the conformal integral itself diverges, and therefore the actual situation is more delicate. The effects of a renormalization counter term are considered, including the associated problem of unitarity violation, such as a Landau-like ghost. Adding (massive or massless) matter fields does not change the picture; to confirm this, detailed calculations were necessary, and they are presented. Some alternative ideas are offered, including a more daring speculation, which is that no counter term should be allowed for at all. This has far-reaching and important consequences, which we discuss. A surprising picture emerges of quantized elementary particles interacting with a gravitational field that is "partly classical". This approach was inspired by a search towards the reconciliation of Hawking radiation with unitarity and locality, and it offers basic new insights there. }, added-at = {2010-09-07T22:09:22.000+0200}, author = {Hooft, Gerard 't}, biburl = {https://www.bibsonomy.org/bibtex/2149827c5d3e4db485f4a18d1b7b84418/jpschaar}, description = {Probing the small distance structure of canonical quantum gravity using the conformal group}, interhash = {1dd0422ab9196d9a1e3b904a598f4ec0}, intrahash = {149827c5d3e4db485f4a18d1b7b84418}, keywords = {quantum spacetime}, note = {cite arxiv:1009.0669 Comment: 20 pages, 1 figure}, timestamp = {2010-09-07T22:09:22.000+0200}, title = {Probing the small distance structure of canonical quantum gravity using the conformal group}, url = {http://arxiv.org/abs/1009.0669}, year = 2010 }