Quantum Gravity: Unification of Principles and Interactions, and Promises of Spectral Geometry

Booss-Bavnbek, Bernhelm

doi:10.3842/sigma.2007.098

Cited by 1 publication

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References 98 publications

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“…From (30) or (31) we obtain for u, ũ the wave equations. Covariant anticommutation relations (13) also follow.…”

Section: Details On Quantization and Graviton Helicitiesmentioning

confidence: 99%

Notes on “Quantum Gravity” and Noncommutative Geometry

Gracia‐Bondía

2010

New Paths Towards Quantum Gravity

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I hesitated for a long time before giving shape to these notes, originally intended for preliminary reading by the attendees to the Summer School "New paths towards quantum gravity" (Holbaek Bay, Denmark, May 2008). At the end, I decide against just selling my mathematical wares, and for a survey, necessarily very selective, but taking a global phenomenological approach to its subject matter. After all, noncommutative geometry does not purport yet to solve the riddle of quantum gravity; it is more of an insurance policy against the probable failure of the other approaches. The plan is as follows: the introduction invites students to the fruitful doubts and conundrums besetting the application of even classical gravity. Next, the first experiments detecting quantum gravitational states inoculate us a healthy dose of scepticism on some of the current ideologies. In Section 3 we look at the action for general relativity as a consequence of gauge theory for quantum tensor fields. Section 4 briefly deals with the unimodular variants. Section 5 arrives at noncommutative geometry. I am convinced that, if this is to play a role in quantum gravity, commutative and noncommutative manifolds must be treated on the same footing; which justifies the place granted to the reconstruction theorem. Together with Section 3, this part constitutes the main body of the notes. Only very summarily at the end of this section we point to some approaches to gravity within the noncommutative realm. The last section delivers a last dose of scepticism. My efforts will have been rewarded if someone from the young generation learns to mistrust current mindsets.

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“…From (30) or (31) we obtain for u, ũ the wave equations. Covariant anticommutation relations (13) also follow.…”

Section: Details On Quantization and Graviton Helicitiesmentioning

confidence: 99%