Oscillatory integrals and the method of stationary phase in infinitely many dimensions, with applications to the classical limit of quantum mechanics I
Oscillatory integrals and the method of stationary phase in infinitely many dimensions, with applications to the classical limit of quantum mechanics I
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无限多维中的振荡积分和固定相方法，及其在量子力学经典极限中的应用 I
DOI：
10.1007/bf01389861
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发表时间：
1977
影响因子：
3.1
通讯作者：
R. Höegh
中科院分区：
文献类型：
--
作者：
S. Albeverio;R. Höegh
我们给出了无限多维振荡积分理论，对于一类相函数，它扩展了有限维理论。特别是，我们将固定相方法、拉格朗日浸没理论和相应的渐近展开扩展到无限维情况。该理论对作者在之前的工作中定义的费曼路径积分的特定应用，产生了以普朗克常数的幂为单位的所有阶量子力学量的渐近展开。
We give a theory of oscillatory integrals in infinitely many dimensions which extends, for a class of phase functions, the finite dimensional theory. In particular we extend the method of stationary phase, the theory of Lagrange immersions and the corresponding asymptotic expansions to the infinite dimensional case. A particular application of the theory to the Feyman path integrals defined in previous work by the authors yields asymptotic expansions to all orders of quantum mechanical quantities in powers of Planck's constant.