Number operators for Riemannian manifolds

Details Number operators for Riemannian manifolds Number operators for Riemannian manifolds

2001-04-17

arxiv.org/abs/math-ph/0104022v1

Physics

Mathematical Physics

17 pages

Scientific paper

The Dirac operator d+delta on the Hodge complex of a Riemannian manifold is regarded as an annihilation operator A. On a weighted space L_mu^2 Omega, [A,A*] acts as multiplication by a positive constant on excited states if and only if the logarithm of the measure density of mu satisfies a pair of equations. The equations are equivalent to the existence of a harmonic distance function on M. Under these conditions N=A*A has spectrum containing the nonnegative integers. Nonflat, nonproduct examples are given. The results are summarized as a quantum version of the Cheeger--Gromoll splitting theorem.

Affiliated with

Also associated with

No associations

Rating

Number operators for Riemannian manifolds does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Number operators for Riemannian manifolds, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Number operators for Riemannian manifolds will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-564541