Hamiltonian dynamics on the moduli space of half weighted Bohr - Sommerfeld Lagrangian subcycles of a fixed volume

Bohr-Sommerfeld-Heisenberg Theory in Geometric Quantization

In the framework of geometric quantization we extend the Bohr-Sommerfeld rules to a full quantization theory which resembles Heisenberg's matrix theory. This extension is possible because Bohr-Sommerfeld rules not only provide an orthogonal basis in the space of quantum states, but also give a lattice structure to this basis. This permits the definition of appropriate shifting operators. As examples, we discuss the 1-dimensional harmonic oscillator and the coadjoint orbits of the rotation group.

Bohr-Sommerfeld-Heisenberg Quantization of the 2-dimensional Harmonic Oscillator

We study geometric quantization of the harmonic oscillator in terms of a singular real polarization given by fibres of the energy momentum map.

Bohr–Sommerfeld拉格朗日态渐近展开中的第一修正项

The First Correction Term in the Asymptotic Expansion of Bohr--Sommerfeld Lagrangian States

本文研究紧致Kähler流形上Bohr–Sommerfeld拉格朗日态的渐近展开，显式计算第一非平凡修正项，并给出$L^2$范数的二阶渐近公式。

$b$-辛环面流形的 Bohr-Sommerfeld 量子化

Bohr-Sommerfeld quantization of $b$-symplectic toric manifolds

本文研究 $b$-辛环面流形的量子化，通过 $T$-模定义 Bohr-Sommerfeld 量子化，证明其与 [GMW18b] 的形式几何量子化一致，且维数等于矩多面体中整点的带符号计数。

Bohr-Sommerfeld tori and relative Poincare series on a complex hyperbolic space

Automorphic forms on a bounded symmetric domain D=G/K can be viewed as holomorphic sections of $L^{\otimes k}$, where L is a quantizing line bundle on a compact quotient of D and k is a positive integer. Let $Γ$ be a cocompact discrete subgroup of SU(n,1) which acts freely on SU(n,1)/U(n). We suggest a construction of relative Poincaré series associated to loxodromic elements in $Γ$. In complex dimension 2 we describe Bohr-Sommerfeld tori in $Γ\backslash SU(n,1)/U(n)$ associated to hyperbolic elements of $Γ$ and prove that the relative Poincaré series associated to the hyperbolic elements of $…

Bohr-Sommerfeld拉格朗日子流形上全纯截面的渐近估计

Asymptotic estimates of holomorphic sections on Bohr-Sommerfeld Lagrangian submanifolds

本文针对满足Bohr-Sommerfeld条件的拉格朗日子流形，给出了全纯截面在其上的范数的渐近估计。