均匀带电的无限长直导线电势问题的正规化处理——一个将量子场论概念与方法融入本科教学的例子

REGULARISATION OF THE POTENTIAL PROBLEM FOR UNIFORMLY CHARGED INFINITELY LONG STRAIGHT WIRES——AN EXAMPLE OF INTEGRATING QUANTUM FIELD THEORY CONCEPTS AND METHODS INTO UNDERGRADUATE TEACHING

若在基础物理课程的教学中合理融入现代物理学研究的概念与方法,则可使学生更好地理解所学知识的应用价值,从而为更高水平的教学和研究作准备。本文以均匀带电无限长直导线电势的计算为例,探讨了如何在本科二年级的电动力学课程教学中引入和渗透现代量子场论的一些概念和方法。具体内容包括良好的数学定义与病态的数学定义、发散积分的正规化、物理量与非物理量等。本文试图以较为浅显的方式来讲明这些对于本科生来说太过抽象的物理与数学概念,以帮助学生在未来学习量子场论等现代物理内容时更轻松自然地理解并使用其中的思想与方法,并对数学与物理中一些一般性的相关问题有更好的理解。

If the concepts and methods of modern physics research are reasonably integrated into the teaching of basic physics courses,students can better understand the application value of what they have learnt,and thus be prepared for higher level teaching and research.In this paper,we take the calculation of the potential of a uniformly charged infinite-length self-con-ducting wire as an example,and discuss how to introduce and penetrate some concepts and methods of modern quantum field theory in the teaching of electrodynamics in the second year of undergraduate courses.Specific contents include good mathematical definitions and patho-logical mathematical definitions,regularisation of divergence integrals,physical quantities and non-physical quantities,and etc.This paper attempts to explain these physics and mathemati-cal concepts that are too abstract for thousands of undergraduate students in a relatively sim-ple way,so as to help students understand and use the ideas and methods more easily and nat-urally when they study modern physics such as quantum field theory in the future,and to have a better understanding of some general problems related to mathematics and physics.