GRAVITY, NONCOMMUTATIVE GEOMETRY AND THE WODZICKI RESIDUE

被引:144
作者
KALAU, W
WALZE, M
机构
[1] Johannes Gutenberg Universität, Institut für Physik
关键词
NONCOMMUTATIVE GEOMETRY; GRAVITY; WODZICKI RESIDUE;
D O I
10.1016/0393-0440(94)00032-Y
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
We derive an action for gravity in the framework of non-commutative geometry by using the Wodzicki residue. We prove that for a Dirac operator D on an n dimensional compact Riemannian manifold with n greater than or equal to 4, n even, the Wodzicki residue Res(D--n+2) is the integral of the second coefficient of the heat kernel expansion of D-2, We use this result to derive a gravity action for commutative geometry which is the usual Einstein-Hilbert action and we also apply our results to a non-commutative extension which is given by the tenser product of the algebra of smooth functions on a manifold and a finite dimensional matrix algebra. In this case we obtain gravity with a cosmological constant.
引用
收藏
页码:327 / 344
页数:18
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