Approaches to Quantum Gravity

Questions and answers 335their vacuum fluctuations which is in conflict with observation unless onestarts fine tuning.2. The case of QCD is a counter example of your statement. QCD is perturbativelyrenormalizable; however, perturbation theory is not applicable to themost important phenomena such as confinement. Your statement is obviouslyinconclusive and we seem to have arrived at a point where only experimentsmay be able to decide. Here I want to remind of an analysis due to T. Damouret al. who numerically showed that within a 15 parameter space of generalizedactions the pure Einstein–Hilbert term is by far the most natural choicewhen comparing with experiment. I am familiar with the Wilsonian approachand of course I completely agree with it.I think we do not disagree on the point that the effective Lagrangean containshigher derivative terms. However, what I want to say is that in a Hamiltonianapproach such as LQG the treatment of the higher derivative action asa fundamental action would be different from what one does usually in theLagrangean counter term framework index quantization path integral. In thelatter approach, these counter terms do not modify the number of degrees offreedom, while in the former they would do. You can see this plainly by lookingat how block spin transformations generate additional effective terms. Youalways integrate out high momentum degrees of freedom with respect to thenaive action, you never change the number of degrees of freedom in the pathintegral measure (in Yang–Mills theories you only use a measure dependingon the connection but not its higher (covariant) derivatives). In the Hamiltonianapproach you would have to face more degrees of freedom. In order toreconcile both approaches, you use the equations of motion of the naive (firstorder) action in order to turn higher derivative terms into lower derivativeterms. I do not care if life is messy, I wanted to point out that the treatmentof effective actions as fundamental Lagrangeans in canonical treatments isinconsistent with the usual treatment. This is how I interpreted your question.• Q-R.Percacci-toE.Livine:Could you elaborate further on the physical significance of the continuous vs.discrete spectrum of the area operator?– A-E.Livine:Loop quantum gravity (LQG) formulates gravity as a gauge theory based onthe compact group SU(2). The Casimir of SU(2) gives the area spectrum.We then get a discrete spectrum. On the other hand, covariant loop quantumgravity (CLQG) has the non-compact Lorentz group as gauge groupand obtains a continuous area spectrum. In three space-time dimensions, thegauge group is actually the Lorentz group, which gives a discrete length