Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1994-06-07
Physics
High Energy Physics
High Energy Physics - Theory
41 pages, LaTeX
Scientific paper
10.1007/BF01231449
Let $X$ be a compact Kahler manifold and $L\to X$ a quantizing holomorphic Hermitian line bundle. To immersed Lagrangian submanifolds $\Lambda$ of $X$ satisfying a Bohr-Sommerfeld condition we associate sequences $\{ |\Lambda, k\rangle \}_{k=1}^\infty$, where $\forall k$ $|\Lambda, k\rangle$ is a holomorphic section of $L^{\otimes k}$. The terms in each sequence concentrate on $\Lambda$, and a sequence itself has a symbol which is a half-form, $\sigma$, on $\Lambda$. We prove estimates, as $k\to\infty$, of the norm squares $\langle \Lambda, k|\Lambda, k\rangle$ in terms of $\int_\Lambda \sigma\overline{\sigma}$. More generally, we show that if $\Lambda_1$ and $\Lambda_2$ are two Bohr-Sommerfeld Lagrangian submanifolds intersecting cleanly, the inner products $\langle\Lambda_1, k|\Lambda_2, k\rangle$ have an asymptotic expansion as $k\to\infty$, the leading coefficient being an integral over the intersection $\Lambda_1\cap\Lambda_2$. Our construction is a quantization scheme of Bohr-Sommerfeld Lagrangian submanifolds of $X$. We prove that the Poincar\'e series on hyperbolic surfaces are a particular case, and therefore obtain estimates of their norms and inner products.
Borthwick David
Paul Thierry
Uribe Alejandro
No associations
LandOfFree
Legendrian Distributions with Applications to Poincaré Series 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 Legendrian Distributions with Applications to Poincaré Series, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Legendrian Distributions with Applications to Poincaré Series will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-421536