标题： 基于新变分原理的阻尼粒子量化 显示英文标题

标题： Quantization of Damping Particle Based On New Variational Principles

摘要： 在本文中，提出了一种新的方法来量化那些运动方程不能转化为哈密顿形式的机械系统。 该方法基于一种新的变分原理，该原理被用来描述一种关系：阻尼粒子可能与一个自由粒子共享一条共同的相轨线，其拉格朗日量在新的变分原理中可以被视为相空间中的拉格朗日量密度。 根据费曼的理论，最小作用量原理被用来修改费曼的路径积分公式，其中拉格朗日量被拉格朗日量密度所替代。 在保守系统的情况下，该修正简化为标准的费曼传播子公式。 作为一个例子，对具有摩擦力的粒子进行了详细分析。 显示英文摘要

摘要： In this paper a new approach is proposed to quantize mechanical systems whose equations of motion can not be put into Hamiltonian form. This approach is based on a new type of variational principle, which is adopted to a describe a relation: a damping particle may shares a common phase curve with a free particle, whose Lagrangian in the new variational principle can be considered as a Lagrangian density in phase space. According to Feynman's theory, the least action principle is adopted to modify the Feynman's path integral formula, where Lagrangian is replaced by Lagrangian density. In the case of conservative systems, the modification reduces to standard Feynman's propagator formula. As an example a particle with friction is analyzed in detail.