论文标题
抗序列的量化，相空间路径积分和符号群的Olshanski半群
Antinormally-Ordered Quantizations, phase space path integrals and the Olshanski semigroup of a symplectic group
论文作者
论文摘要
本文的主要目的是显示以下三个概念之间的一些亲密关系：（1）$ sp（2n，2n，\ mathbb {r}）$的互惠表示，并将其扩展到某些semigroups，称为olshanski semigroup $ sp（2n，\ mathbb {r}）$ semigrizatiz $ semigrimatized semigrimed onsecterart（2） $ \ mathbb {r}^{2M} \ cong \ mathbb {c}^{m} $，（3）路径积分量化，其中路径在相位空间上的路径$ \ mathbb {r}^{2m}^{2M} {2M} \ cong \ cong \ cong \ mathbb {c}^c}^m} $。在主要定理中，互惠表示$ρ（e^{x}）$（$ x \ in \ mathfrak {sp}（sp}（2n，2n，\ mathbb {r}）$）以通用的feynman-feynman-feynman--kac（-kac（-kac）（ - it不），但以实时的（非imiminaly gimiminaly gimimalional intemal intemal intemal nemptal fime nembalal firmalal fime nemberal fime nemberal fimational intemal intemal intemal fime time）表示。 Olshanski Semigroups在其证明中扮演着领导角色。
The main aim of this article is to show some intimate relations among the following three notions: (1) the metaplectic representation of $Sp(2n,\mathbb{R})$ and its extension to some semigroups, called the Olshanski semigroup for $Sp(2n,\mathbb{R})$ or Howe's oscillator semigroup, (2) antinormally-ordered quantizations on the phase space $\mathbb{R}^{2m}\cong\mathbb{C}^{m}$, (3) path integral quantizations where the paths are on the phase space $\mathbb{R}^{2m}\cong\mathbb{C}^{m}$. In the Main Theorem, the metaplectic representation $ρ(e^{X})$ ($X\in\mathfrak{sp}(2n,\mathbb{R})$) is expressed in terms of generalized Feynman--Kac(--Itô) formulas, but in real-time (not imaginary-time) path integral form. Olshanski semigroups play the leading role in the proof of it.
