Topological calculation of the phase of the determinant of a non self-adjoint elliptic operator

Details Topological calculation of the phase of the determinant of a non self-adjoint elliptic operator Topological calculation of the phase of the determinant of a non self-adjoint elliptic operator

2004-01-19

arxiv.org/abs/math-ph/0401037v2

Commun.Math.Phys. 259 (2005) 287-305

Physics

Mathematical Physics

To appear in Communications of Mathematical Physics

Scientific paper

10.1007/s00220-005-1394-6

We study the zeta-regularized determinant of a non self-adjoint elliptic operator on a closed odd-dimensional manifold. We show that, if the spectrum of the operator is symmetric with respect to the imaginary axis, then the determinant is real and its sign is determined by the parity of the number of the eigenvalues of the operator, which lie on the positive part of the imaginary axis. It follows that, for many geometrically defined operators, the phase of the determinant is a topological invariant. In numerous examples, coming from geometry and physics, we calculate the phase of the determinants in purely topological terms. Some of those examples were known in physical literature, but no mathematically rigorous proofs and no general theory were available until now.

Affiliated with

Also associated with

No associations

Rating

Topological calculation of the phase of the determinant of a non self-adjoint elliptic operator 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 Topological calculation of the phase of the determinant of a non self-adjoint elliptic operator, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Topological calculation of the phase of the determinant of a non self-adjoint elliptic operator will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-392625