偶Poisson结构到密度代数的正则提升的存在性

辛群体上的结合半密度与量子化

Associative half-densities on symplectic groupoids and quantization

本文研究了满足适当结合条件的半密度，用于增强辛群体上的乘法映射，以实现对庞加莱-诺维科夫结构的完全半经典-解析近似。文章展示了此类结合半密度的存在性和分类，并将其应用于理解康特赛维奇量子化公式中的半经典因子。在线性泊松结构的情况下，恢复了杜福同态及其卡西瓦拉-韦尔内扩展中出现的因子作为规范的结合增强。

Solution to the modified Helmholtz equation for arbitrary periodic charge densities

We present a general method for solving the modified Helmholtz equation without shape approximation for an arbitrary periodic charge distribution, whose solution is known as the Yukawa potential or the screened Coulomb potential. The method is an extension of Weinert's pseudo-charge method [M. Weinert, J. Math. Phys. 22, 2433 (1981)] for solving the Poisson equation for the same class of charge density distributions. The inherent differences between the Poisson and the modified Helmholtz equation are in their respective radial solutions. These are polynomial functions, for the Poisson equation…

关于奇Laplace算子

On odd Laplace operators

考虑奇Poisson（= Schouten）流形$M$上作用于不同权密度的奇Laplace算子.我们证明了密度的重量1/2（半密度）的情况下，区分的存在唯一的奇拉普拉斯算子只依赖于一个点的“轨道空间”的体积形式。这包括早期的结果奇辛的情况下，有一个典型的奇拉普拉斯半密度。$M$上的体积形式的空间被一个自然广群划分成轨道，该广群的箭头对应于量子Batalin-Vilkovisky方程的解。我们给出了一个比较与黎曼流形，甚至泊松流形的情况。特别是，奇拉普拉斯算子的平方恰好是一个泊松向量场，定义了温斯坦的“模类”的一个模拟。

Brane quantization of toric Poisson varieties

In this paper we propose a noncommutative generalization of the relationship between compact Kähler manifolds and complex projective algebraic varieties. Beginning with a prequantized Kähler structure, we use a holomorphic Poisson tensor to deform the underlying complex structure into a generalized complex structure, such that the prequantum line bundle and its tensor powers deform to a sequence of generalized complex branes. Taking homomorphisms between the resulting branes, we obtain a noncommutative deformation of the homogeneous coordinate ring. As a proof of concept, this is implemented f…

Flat bi-Hamiltonian structures and invariant densities

A bi-Hamiltonian structure is a pair of Poisson structures $\mathcal P$, $\mathcal Q$ which are compatible, meaning that any linear combination $α\mathcal P + β\mathcal Q$ is again a Poisson structure. A bi-Hamiltonian structure $(\mathcal P, \mathcal Q)$ is called flat if $\mathcal P$ and $\mathcal Q$ can be simultaneously brought to a constant form in a neighborhood of a generic point. We prove that a generic bi-Hamiltonian structure $(\mathcal P, \mathcal Q)$ on an odd-dimensional manifold is flat if and only if there exists a local density which is preserved by all vector fields Hamiltonia…

主 bundle 中通过结构群子群的李-泊松约简

Lie-Poisson reduction in principal bundles by a subgroup of the structure group

研究主 bundle 的多辛 bundle 上的哈密顿场论，通过子群 H 的不变哈密顿密度进行约简，推导约简后的可观测量、括号和运动方程，提出通过子群的李-泊松约简方法，并通过重建成问题和实例展示框架。

具有特定单粒子密度和对粒子密度的粒子分布的构造

On the Construction of Particle Distributions with Specified Single and Pair Densities

我们讨论的概率分布的粒子配置的$d$维，即一个点过程，与指定的密度$ρ$和径向分布函数$g({\bf r})$的存在的必要条件。在$d=1$中，我们给出了关于$ρg({\bf r})$的更新（Markov）型点过程存在的充要条件.证明了对于$g(r) = 0, r < D$和$g(r) = 1, r > D$满足这些条件，当且仅当$ρD \leq e^{-1}$：稀释泊松过程可获得的最大密度.然后，我们简要地描述必要和充分条件，有效的在每一个层面上，$ρg(r)$指定一个行列式点过程，所有的$n$ -粒子密度，$ρ_n({\bf r}_1, ..., {\bf r}_n)$，明确给出的决定因素。我们举几个例子。