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이승국 한국물리학회 2002 새물리 Vol.44 No.3
The U(1) dual fiber bundle formalism of electromagnetism is discussed. We see that electromagnetism can equally well be described in terms of either formalism. 자기류(magnetic current)의 존재는 맥스웰 방정식의 이중변환 불변성을 보여주며 전기전하의 양자화에 대한 이해를 돕는다. 이는 1930년대 Dirac에 의해 자기전하 $g_{M}$을 갖는 자기홀극의 가정으로부터 시작되었다. 그는 벡터 퍼텐셜의 특이점들로 만들어진 무한히 긴 끈의 끝에 자기홀극을 가정하는 형식을 빌어 이를 설명하였으며 전기전하와 자기전하 사이에 $qg_{M}$=${{1}\over{2}}n\hbar{c}$, $n$:정수의 관계가 만족됨을 보였다\cite{1}. Schwinger는 무한히 긴 끈의 중심에 자기홀극을 위치시키는 형식을 통해 $qg_{M}$=$n\hbar{c}$의 결과를 얻었다\cite{2}. 그 뒤 Wu와 Yang은 특이점 끈을 제거하고 단순한 직교공간의 일반화를 의미 하는 수학적 이론인 bundle이론을 이용하여 자기홀극이 U(1)을 structure group으로 갖는 non-trivial principal fiber bundle로 표현됨을 보였다. 즉, 자기홀극에 의한 벡터 퍼텐셜을 정의하기 위해 최소한 둘 이상의 open set이 필요함을 보였다\cite{3}. 막스웰 방정식과 로렌츠 방정식은 자기홀극이 존재할 때 다음의 이중성 변환에 대해 불변이다
이승국 한국아동교육학회 1999 아동교육 Vol.8 No.1
Education is not accomplished just through learning or modeling because education implies flexibility in the process teaching and learning. The flexibility complies physical punishment among other things. There has been controversies about the justification of physical punishment for a long time. When we find physical punishment unavoidable, we should bear in mind that it should imply "love" for the victim as well as some educational purposes. As a good model of human being, the teacher must influence the student morally in the process of punishing. When we discuss the effects of physical punishment, we should not judge each case with its motif alone nor should we evaluate only the result. We also should not fall into the fallacy of generalizing the effects of physical punishment with some specific cases or small number of instances. Physical punishment has been accepted as a way of education throughout the history in the world. Parents who over--protect their children are hurting the authority of teachers who are at a loss what to do with their students' misbehavior. I suggest that it is desirable to leave the physical punishment to the choice of teachers for the moral or intellectual growth of students, who are becoming less and less strong and intolerant physically as well as mentally these days.I also suggest that teachers and parents should co-operate with each other to establish the educational environment in which we need no punishment.