A generalized Lichnerowicz formula, the Wodzicki residue and gravity
Abstract
We prove a generalized version of the wellknown Lichnerowicz formula for the square of the most general Dirac operator ovtilde D on an evendimensional spin manifold associated to a metric connection ovtilde▿. We use this formula to compute the subleading term Φ _{1}(x, x, overlineD^{2}) of the heatkernel expansion of ovtilde D^{2}. The trace of this term plays a key role in the definition of a (euclidian) gravity action in the context of noncommutative geometry. We show that this gravity action can be interpreted as defining a modified euclidian EinsteinCartan theory.
 Publication:

Journal of Geometry and Physics
 Pub Date:
 June 1996
 DOI:
 10.1016/03930440(95)000305
 arXiv:
 arXiv:hepth/9503152
 Bibcode:
 1996JGP....19..143A
 Keywords:

 High Energy Physics  Theory
 EPrint:
 10 pages, plain tex