Furthermore, this is an assumption that
*fails*
in conventional quantum field theory, because in that context
well defined operators and finite norm states need to be smeared
in at least three dimensions, and one-dimensional objects are too
singular.
The fact that at the basis of loop gravity there is a
mathematical assumption that fails for conventional Yang-Mills
quantum field theory is probably at the origin of some of the
resistance that loop quantum gravity encounters among some high
energy theorists. What distinguishes gravity from Yang-Mills
theories, however, and makes this assumption viable in gravity,
even if it fails for Yang-Mills theory, is diffeomorphism
invariance. The loop states are singular states that span a
``huge'' non-separable state space. (Non-perturbative)
diffeomorphism invariance plays two roles. First, it wipes away
the infinite redundancy. Second, it ``smears'' a loop state into
a knot state, so that the physical states are not really
concentrated in one dimension, but are, in a sense, smeared all
over the entire manifold by the nonperturbative diffeomorphisms.
This will be more clear in the next section.

Loop Quantum Gravity
Carlo Rovelli
http://www.livingreviews.org/lrr-1998-1
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