大学物理和场论课程中的协变性浅谈

ON THE TEACHING OF COVARIANCE IN COLLEGE PHYSICS AND FIELD THEORY

本文主要论述了物理量的协变性质在大学物理和场论教学中的重要性。首先以图示的办法形象地讲解电磁场的洛伦兹变换,同时指出协变性的理解可以使学生更加深刻理解电磁学理论的本质。论文证明n阶反对称张量在行列式为1的矩阵变换下是不变的,因此四阶反对称张量ε^(μνρσ)自然是协变的,矢量和轴矢量的镜像变换性质是不一样的。论文还指出协变性是对物理公式变换性质的表述,物理量会因为形式不同而有不同的协变性的理解。论文以场论散射截面的协变性质为例,指出不同理解的差别与联系。

This paper mainly talked about the importance of covariance in the course of college physics and field theory. We used a figure to show that how to understand the Lorentz Transformation at the end of the course of Electromagnatics. Then we showed that Levi-Civita antisymmetric tensor is invariant under a transformation matrix which determinant equals one, thus ε^μνρσ is a Lorentz covariant tensor, vector and axial-vector have different mirror transformation. At last, we argued that a physical variable will have different properties of covarianee under different formulation. As a demonstration, we showed the difference and the relation in the understanding on the cross section in quantum field theory.