Editing Loop quantum gravity (section)

== History ==
{{Main|History of loop quantum gravity}}

In 1986, [[Abhay Ashtekar]] reformulated Einstein's general relativity in a language closer to that of the rest of fundamental physics, specifically [[Yang–Mills theory]].<ref>{{cite journal |last1=Ashtekar |first1=Abhay |title=New Variables for Classical and Quantum Gravity |journal=Physical Review Letters |date=3 November 1986 |volume=57 |issue=18 |pages=2244–2247 |doi=10.1103/PhysRevLett.57.2244 |pmid=10033673 |bibcode=1986PhRvL..57.2244A |url=https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.57.2244}}</ref> Shortly after, [[Ted Jacobson]] and [[Lee Smolin]] realized that the formal equation of quantum gravity, called the [[Wheeler–DeWitt equation]], admitted solutions labelled by loops when rewritten in the new [[Ashtekar variables]]. [[Carlo Rovelli]] and Smolin defined a [[nonperturbative]] and background-independent quantum theory of gravity in terms of these loop solutions. [[Jorge Pullin]] and [[Jerzy Lewandowski]] understood that the intersections of the loops are essential for the consistency of the theory, and the theory should be formulated in terms of intersecting loops, or [[Graph (discrete mathematics)|graphs]].

In 1994, Rovelli and Smolin showed that the quantum [[operator (physics)|operators]] of the theory associated to area and volume have a discrete spectrum.<ref>{{cite journal |title = Discreteness of area and volume in quantum gravity |last1 = Rovelli |first1 = Carlo |last2 = Smolin |first2 = Lee |author1-link = Carlo Rovelli |author2-link = Lee Smolin |journal = [[Nuclear Physics B]] |year = 1995 |volume = 442 |issue = 3 |pages = 593–619 |doi = 10.1016/0550-3213(95)00150-Q|arxiv = gr-qc/9411005 |bibcode = 1995NuPhB.442..593R }}</ref> That is, geometry is quantized. This result defines an explicit basis of states of quantum geometry, which turned out to be labelled by [[Roger Penrose]]'s [[spin network]]s, which are [[Graph (discrete mathematics)|graphs]] labelled by [[Spin (physics)|spins]].

The canonical version of the dynamics was established by Thomas Thiemann, who defined an anomaly-free [[Hamiltonian (quantum mechanics)|Hamiltonian]] operator and showed the existence of a mathematically consistent background-independent theory. The covariant, or "spin foam", version of the dynamics was developed jointly over several decades by research groups in France, Canada, UK, Poland, and Germany. It was completed in 2008, leading to the definition of a family of transition amplitudes, which in the [[classical limit]] can be shown to be related to a family of truncations of general relativity.{{sfn|Rovelli|2011}} The finiteness of these amplitudes was proven in 2011.{{sfn|Muxin|2011|p=064010}}{{sfn|Fairbairn|Meusburger|2011}} It requires the existence of a positive [[cosmological constant]], which is consistent with observed [[Accelerating universe|acceleration in the expansion of the Universe]].