Editing Ashtekar variables (section)

{{Short description|Variables used in general relativity}}
{{main|Frame fields in general relativity|spin connection|Self-dual Palatini action}}
In the [[ADM formulation]] of [[general relativity]], spacetime is split into spatial slices and a time axis. The basic variables are taken to be the [[induced metric]] <math>q_{ab} (x)</math> on the spatial slice and the metric's conjugate momentum <math>K^{ab} (x)</math>, which is related to the [[extrinsic curvature]] and is a measure of how the induced metric evolves in time.<ref>{{cite book |title=[[Gravitation (book)|Gravitation]] |first=Charles W. |last=Misner |first2=Kip S. |last2=Thorne |first3=John Archibald |last3=Wheeler |publisher=W. H. Freeman and Company |location=New York |isbn= }}</ref> These are the metric [[canonical coordinates]].

In 1986 [[Abhay Ashtekar]] introduced a new set of canonical variables, '''Ashtekar''' ('''new''') '''variables''' to represent an unusual way of rewriting the metric canonical variables on the three-dimensional spatial slices in terms of an [[SU(2)]] [[gauge field]] and its complementary variable.<ref>{{cite journal | last1 = Ashtekar | first1 = A | year = 1986 | title =  New variables for classical and quantum gravity| journal = Physical Review Letters | volume = 57 | issue = 18| pages = 2244–2247 | doi=10.1103/physrevlett.57.2244 | pmid=10033673|bibcode = 1986PhRvL..57.2244A }}</ref>