AI 中文总结
该研究在Bargmann-Fock和薛定谔模型中，利用梅塔普lectic表示算子与海森堡表示的交错性质，推导并刻画了梅塔普lectic核的微分形式，明确其为辛变换对应的经典高斯函数。
AI 中文摘要
我们仅基于梅塔普lectic表示算子与海森堡表示的定义交错性质，在Bargmann-Fock模型中推导该算子的积分核。将梅塔普lectic算子表示为积分算子，可将对应的无穷小交错恒等式转化为其核满足的一阶偏微分方程组。我们证明该方程组（在单位标量范围内）唯一确定核，此核正是与辛变换相关的经典高斯函数，对薛定谔模型也得到了类似结果。
英文摘要
We present a derivation of the integral kernel of a metaplectic representation operator in the Bargmann-Fock model based solely on its defining intertwining property with the Heisenberg representation. Expressing a metaplectic operator as an integral operator transforms the corresponding infinitesimal intertwining identities into a system of first-order partial differential equations satisfied by its kernel. We show that this system determines the kernel (up to a unit scalar) which is precisely the classical Gaussian associated with the symplectic transformation. A similar result is obtained for the Schrödinger model.
