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1992 Classical limit: weaves
Ashtekar, Rovelli, Smolin.
The first indication that the theory predicts Planck
scale discreteness came from studying the states
that approximate geometries flat on large scale [23].
These states, denoted “weaves”, have a “polymer”
like structure at short scale, and can be viewed as
a formalization of Wheeler’s “spacetime foam”.
……
1994 Discreteness of area and volume eigenvalues
Rovelli, Smolin.
In my opinion, the most significative result of loop
quantum gravity is the discovery that certain ge-
ometrical quantities, in particular area and vol-
ume, are represented by operators that have dis-
crete eigenvalues. This was found by Rovelli and
Smolin in [186], where the first set of these eigenval-
ues were computed. Shortly after, this result was
confirmed and extended by a number of authors,
using very diverse techniques. In particular, Re-
nate Loll [142,143] used lattice techniques to ana-
lyze the volume operator and corrected a numerical
error in [186]. Ashtekar and Lewandowski [138,17]
recovered and completed the computation of the
spectrum of the area using the connection represen-
tation, and new regularization techniques. Frittelli,
Lehner and Rovelli [84] recovered the Ashtekar-
Lewandowski terms of the spectrum of the area,
using the loop representation. DePietri and Rov-
elli [77] computed general eigenvalues of the vol-
ume. Complete understanding of the precise rela-
tion between different versions of the volume oper-
ator came from the work of Lewandowski [139].
……
1996 Black hole entropy
Krasnov, Rovelli.
A derivation of the Bekenstein-Hawking formula for
the entropy of a black hole from loop quantum grav-
ity was obtained in [176], on the basis of the ideas of
Kirill Krasnov [134,135]. Recently, Ashtekar, Baez,
Corichi and Krasnov have announced an alterna-
tive derivation [11].
1997 Sum over surfaces
Reisenberger Rovelli.
A “sum over histories” spacetime formulation of
loop quantum gravity was derived in [181,160]
from the canonical theory. The resulting covari-
ant theory turns out to be a sum over topologically
inequivalent surfaces, realizing earlier suggestions
by Baez [26,27,31,25], Reisenberger [159,158] and
Iwasaki [124] that a covariant version of loop grav-
ity should look like a theory of surfaces. Baez has
studied the general structure of theories defined in
this manner [33]. Smolin and Markoupolou have
explored the extension of the construction to the
Lorentzian case, and the possibility of altering the
spin network evolution rules [144].
