Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2008-08-18
Commun.Math.Phys.293:205-230,2010
Physics
High Energy Physics
High Energy Physics - Theory
27 pages
Scientific paper
10.1007/s00220-009-0915-0
We rederive the expansion of the Bergman kernel on Kahler manifolds developed by Tian, Yau, Zelditch, Lu and Catlin, using path integral and perturbation theory, and generalize it to supersymmetric quantum mechanics. One physics interpretation of this result is as an expansion of the projector of wave functions on the lowest Landau level, in the special case that the magnetic field is proportional to the Kahler form. This is relevant for the quantum Hall effect in curved space, and for its higher dimensional generalizations. Other applications include the theory of coherent states, the study of balanced metrics, noncommutative field theory, and a conjecture on metrics in black hole backgrounds. We give a short overview of these various topics. From a conceptual point of view, this expansion is noteworthy as it is a geometric expansion, somewhat similar to the DeWitt-Seeley-Gilkey et al short time expansion for the heat kernel, but in this case describing the long time limit, without depending on supersymmetry.
Douglas Michael R.
Klevtsov Semyon
No associations
LandOfFree
Bergman Kernel from Path Integral 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 Bergman Kernel from Path Integral, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Bergman Kernel from Path Integral will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-698799