Stochastic variational method as quantization scheme: Field quantization of the complex Klein–Gordon equation
Stochastic variational method as quantization scheme: Field quantization of the complex Klein–Gordon equation
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随机变分法作为量化方案：复 Klein-Gordon 方程的场量化
DOI：
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发表时间：
2013
期刊：
影响因子：
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通讯作者：
Takeshi Kodama
中科院分区：
文献类型：
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作者：
Tomoi Koide;Takeshi Kodama
随机变分方法是变分方法在随机变量情形下的推广。在该系列论文中，我们研究了SVM作为替代场量化方案的适用性。在这里，我们讨论复杂的Klein-Gordon方程。在该方案中，随机场的欧拉-拉格朗日方程导致泛函薛定谔方程，而泛函薛定谔方程又可以被解释为泛函空间中的理想流体方程。我们表明，Fock态矢量是由这些微分方程的定态解给出的，并且可以再现通常正则量子化中的各种结果，包括反粒子的影响。本公式是一个基于可交换变量的量子化方案，因此不会出现与算子排序相关的模糊性，例如在Noether电荷的定义中。
Stochastic Variational Method (SVM) is the generalization of the variation method to the case with stochastic variables. In the series of papers, we investigate the applicability of SVM as an alternative field quantization scheme. Here, we discuss the complex Klein-Gordon equation. In this scheme, the Euler-Lagrangian equation for the stochastic fields leads to the functional Schroedinger equation, which in turn can be interpreted as the ideal fluid equation in the functional space. We show that the Fock state vector is given by the stationary solution of these differential equations and various results in the usual canonical quantization can be reproduced, including the effect of anti-particles. The present formulation is a quantization scheme based on commutable variables, so that there appears no ambiguity associated with the ordering of operators, for example, in the definition of Noether charges.