Number operators for Riemannian manifolds

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dc.creatorBueler, Ed
dc.date2001-04-17
dc.date.accessioned2026-07-25T22:15:48Z
dc.descriptionThe 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.
dc.description17 pages
dc.identifierhttps://arxiv.org/abs/math-ph/0104022
dc.identifierhttp://arxiv.org/abs/math-ph/0104022
dc.identifier.urihttps://dspace.dare.co.zw/handle/123456789/87392
dc.subjectMathematical Physics
dc.subjectDifferential Geometry
dc.subject58J50; 81S10
dc.titleNumber operators for Riemannian manifolds
dc.typetext

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