相对论带电费密子Liouville方程  

LIOUVILLE EQUATION OF RELATIVISTIC CHARGED FERMION

作　　者：王仁川[1] 朱栋培[1] 黄卓然 柯治民 

机构地区：[1]中国科学技术大学天体物理中心,中国科学技术大学近代物理系,美国橡树岭国家实验室,美国德州A&M大学物理系回旋加速器研究所与理论物理中心,合肥,230026

出　　处：《物理学报》1991年第1期14-24,共11页Acta Physica Sinica

基　　金：美国能源部核物理局编号为DR-ACO5840R21400合同以及美国国家科学基金编号为NSF 86-08149合同的资助

摘　　要：作为密度矩阵一种形式的Wigner函数是量子相空间里的分布。用它描述相对论费密子时,它的通常表达形式为4×4矩阵函数。本文得到相对论带电费密子的2×2矩阵形式的Wigner函数以及它所满足的Liouville方程。这一方程与量子电动力学里带电费密子满足的Dirac方程完全等价。在描述中能核碰撞的Walecka模型里,当只有矢量介子(或标量介于取平均场近似)时,核子满足一定形式的Dirac方程。本文的方程也与之等价。还证明了(2×2)Wigner函数与相对论费密子的波函数在描述量子体系上起着同样的作用。量子体系的可观察量的全部知识都可以通过这里的Wigner函数得到。As a form of density matrix, the Wigner function is the distribution in quantum phase space. It is a 2×2 matrix function when one uses it to describe the non-relativistic fermion. While describing the relativistic fermion, it is usually represented by 4×4 matrix function. In this paper we obtain a Wigner function for the relativistic fermion in the form of 2×2 matrix, and the Liouville equation satisfied by the Wigner function. This equation is equivalent to the Dirac equation of charged fermion in QED. Our equation is also equivalent to the Dirac equation in the Walecka model applied to the intermediate energy nuclear collision while the nucleon is coupled to the vector meson only (or taking mean field approximation for the scalar meson). We prove that our 2×2 Wigner function completely describes the quantum system just the same as the relativistic fermion wave function. All the information about the observables can be obtained with our Wigner function.

关 键 词：相对论 带电费密子 LIOUVILLE 方程 

分 类 号：O413[理学—理论物理]