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#2294 07/19/05 11:16 AM
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Quote:
Originally posted by Pasti:
Ibliss:"The natural explanation is that the standard model is an effective field theory which describes degrees of freedom of nature below some cutoff momentum."

Yes,true,or below some energy. However, this explanation does not apply to renormalizability. But is such an explanation natural, or is it an a posteriori explanation, a justification of sorts?Is it fact or technique?
Alternatively, think about quantum gravity.Perturbatively it is non-renormalizable, and furthermore, you need to impose cutoffs. But as far as LQG goes, the cutoffs are present in the theory since the area and volume operator are quantized.


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#2295 07/19/05 06:03 PM
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Quote:
Originally posted by LAXMIKANT:
Quote:
Originally posted by Pasti:
Ibliss:"The natural explanation is that the standard model is an effective field theory which describes degrees of freedom of nature below some cutoff momentum."

Yes,true,or below some energy. However, this explanation does not apply to renormalizability. But is such an explanation natural, or is it an a posteriori explanation, a justification of sorts?Is it fact or technique? Alternatively, think about quantum gravity.Perturbatively it is non-renormalizable, and furthermore, you need to impose cutoffs. But as far as LQG goes, the cutoffs are present in the theory since the area and volume operator are quantized.
Yes, this is an interesting topic wink I don't know too much about QG. But to me it doesn't sound surprising at all that gravity should be nonrenormalizable. If you take some well defined statistical mechanical model defined on some lattice and you look at the scaling limit, then that model can usually described by some field theory. The details about the type of lattice correspond to operators that are ''non renormalizable'' in the field theory language.

#2296 07/19/05 06:21 PM
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Ibliss, gravity is non-renormalizable only perturbatively, i.e. if you expand the metric in "series" about some background metric. At least, this is 't Hooft argument. However, this is not the case if you attempt to quantize it non-perturbatively, like in LQG. In LQG, at hte very least at the kinematical level, since the area and volume are quantized, this provides a natural UV regulator. This is the major difference between lattice field theory and LQG (or lattice LQG if you like it better).

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