A new perspective on functional integration
A new perspective on functional integration
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功能集成的新视角
DOI：
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发表时间：
1995
期刊：
影响因子：
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通讯作者：
C. DeWitt
中科院分区：
文献类型：
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作者：
P. Cartier;C. DeWitt
本文的核心是具有大量专业化的一般定理。给定一个流形 N 和有限数量的 N 上点变换的单参数组，其中生成器 Y,X(1),...,X(d)，通过 N 上指向路径（具有一个固定点的路径）空间的函数积分，我们获得作用于 N 上张量或旋量场的函数算子的单参数组。该组的生成器是 X(α) 方向上的李导数 LX(α) 的二次形式加上 LY 中的线性项。基本函数积分在 L2,1 路径 x:T→N（具有平方可积一阶导数的连续路径）上。尽管积分器在时间平移下是不变的，但积分功能足够强大，可以用于非时间平移不变的系统。给出了基本公式的七个重要应用，并计算了半经典展开式。证明方法非常严格，并将 Albeverio-Ho/egh-Krohn 振荡积分与 Elworthy 的参数结合起来......
The core of this article is a general theorem with a large number of specializations. Given a manifold N and a finite number of one‐parameter groups of point transformations on N with generators Y,X(1),...,X(d), we obtain, via functional integration over spaces of pointed paths on N (paths with one fixed point), a one‐parameter group of functional operators acting on tensor or spinor fields on N. The generator of this group is a quadratic form in the Lie derivatives LX(α) in the X(α)‐direction plus a term linear in LY. The basic functional integral is over L2,1 paths x:T→N (continuous paths with square integrable first derivative). Although the integrator is invariant under time translation, the integral is powerful enough to be used for systems which are not time translation invariant. Seven nontrivial applications of the basic formula are given, and the semiclassical expansion is computed. The methods of proof are rigorous and combine Albeverio–Ho/egh‐Krohn oscillatory integrals with Elworthy’s parametr...