Why we cant resolve nonrenormalization problem in gravitation by freely adding?

[ndung200790]

Please teach me this:
Why we can not resolve the nonrenormalization problem in quantum gravity by freely adding the counterterms with bare parameters nonzero but the corresponding physical parameters being zero.
Thank you very much in advanced.

 

[ndung200790]

At the moment,I have just understood that in gravity field theory(quantum) the number of divergent diagrams is infinite,then the procedure is impossible.

 

[Finbar]

One can always introduce more and more counter terms in order to cancel divergences such that observables( e.g. renormalized couplings) remain finite. The problem with perturbative gravity is that the counter terms will not have the same form as the original action so new couplings have to be introduced at every order. These couplings then correspond to more observables that must be fixed by experiment. Since there will be an infinite number the theory isn't predictive at least as a fundamental theory.

On the other hand one can still treat perturbative gravity as an effective theory at low energies (http://arxiv.org/pdf/gr-qc/0311082v1) because one can show that the new couplings that have to be introduced are suppressed by the Planck mass. So the theory can still be predictive as long as E/M_pl is small where E is the energy scale of the experiment and M_pl is the Planck mass.


I hope that's useful.

 

[Demystifier]

Why we can not resolve the nonrenormalization problem in quantum gravity by freely adding the counterterms with bare parameters nonzero but the corresponding physical parameters being zero.

There is no any physical reason why would these physical parameters be zero. Indeed, a high-energy experiment would probably reveal that they are not zero.

 

[ndung200790]

Thank you very much again!