QUANTUM PHYSICS; PARTICLES AND FIELDS 535 Path integrals for spinning particles, stationary phase and the Duistermaat-Heckmann theorem
QUANTUM PHYSICS; PARTICLES AND FIELDS 535 Path integrals for spinning particles, stationary phase and the Duistermaat-Heckmann theorem
复制标题
量子物理学;
DOI：
--
复制
发表时间：
1996
期刊：
影响因子：
--
通讯作者：
O. T. Turgut
中科院分区：
文献类型：
--
作者：
E. Ercolessi;G. Morandi;F. Napoli;P. Pieri;J. M. Guilarte;K. Fujii;T. Kashiwa;S. Sakoda;S. Giller;C. Gonera;T. Iwai;Y. Uwano;N. Katayama;D. McMullan;I. Tsutsui;S. Rajeev;O. T. Turgut
我们在经典和量子水平上研究了自旋粒子在外场中的传播子和配分函数的评估问题，并与断言的定相近似的准确性有关。在经典水平上，我们认为这种近似的准确性源于这样一个事实，即磁场中自旋粒子（在两球S2上）的动力学是R4上线性动力系统从R4到S2的约化。然而，在量子水平上，在路径积分方法中，使用固定相位近似固有的限制，规则路径与进入路径积分的动作中不存在调节器这一事实相冲突。这被证明会导致路径积分的前因子是严格发散的，除了经典极限。与文献中提出的各种方法进行了关键的比较。给出的公式的有效性…
We examine the problem of the evaluation of both the propagator and of the partition function of a spinning particle in an external field at the classical as well as the quantum level, in connection with the asserted exactness of the stationary phase approximation. At the classical level we argue that exactness of this approximation stems from the fact that the dynamics (on the two‐sphere S2) of a spinning particle in a magnetic field is the reduction from R4 to S2 of a linear dynamical system on R4. At the quantum level, however, and within the path integral approach, the restriction, inherent to the use of the stationary phase approximation, to regular paths clashes with the fact that no regulators are present in the action that enters the path integral. This is shown to lead to a prefactor for the path integral that is strictly divergent, except in the classical limit. A critical comparison is made with the various approaches that have been presented in the literature. The validity of a formula given i...