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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”.

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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].

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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].