| [ sciEncE ] in KIDS 글 쓴 이(By): soliton (김 찬주) 날 짜 (Date): 2000년 9월 19일 화요일 오후 02시 10분 05초 제 목(Title): Re: Question! Physics! >Then, an example of a gauge transformation is to move each >fiber (or each straw) upward or downward. You can move each >of them by an arbitrary amount (stupid physicists call this "local gauge >transformation", unlike we, the mathematicians). Now after this 앗! H. Weyl이 "stupid physicist"라는 말씀이신가요? 여태까지 저는 "clever mathematician"으로 알고 있었는데요. 그렇다면, stupid physicist = clever mathematician ?? 물론 농담입니다 :) >Going to a non-trivial example, imagine a four dimensional space-time >we are living in. Now at each point of the space-time, place a >four dimensional vector (now we're talking about a vector bundle). >Now one decides to "see" only the x and y components of each vector. >Upon this agreement, the rotation of each vector along the "circle" (whose >center is located at the point where we placed the vector) parallel to >the (t,z) plane does not change the whole bundle geometry. Now the >gauge transformation in this context is the aforementioned rotation >of each vector by an arbitrary amount, or in other words, the gauge >transformations form an abelian (or U(1)) group. This construction, >in the end, corresponds to an "over-simplified" version of the U(1) gauge >theory (or Maxwell's electromagnetism). 설명을 시작하신 김에 connection까지 얘기하셨으면 좋았을텐데요. "over-simplified"라고는 하셨어도 photon field(connection)가 없는 "전자기학"은 조금 이상하군요. --------------------------------- >ha.... this is very neat explanation! but why "dumb" physicists (i think they >are smart but let just pretend they are dumb kiki.... ) call it "local" ? is >that mean there is also "global" gauge transform? it begs me a question. ^^ > .............. >i like Mr. soliton's explanation better. so it simply means when you have a >certain tensor and >this tensor doesn't change under a certain transformation of its components, >then it is called gauge invariant! OK. i got that. now why people call it >"gauge"? who was the first person to name it? gauge means "measurement" right? 위에서 썼듯이 clever mathematician(or stupid physicist)인 H. Weyl이 gauge theoy라는 말을 만든 사람이죠. 아인시타인의 일반 상대론에 영향을 받아서 전자기학도 비슷하게 해볼 수 있지 않을까 하고 (당시로서는 헛된) 노력을 많이 했습니다. 그 와중에 gauge라는 용어를 도입했구요. 본래 중력을 염두에 두고 개념을 만들어보려고 했기 때문에 "gauge"라는 용어를 쓰게 되었죠. (space-time의 scale change를 A_\mu하고 관련을 시키려고 했습니다. scale change라는 것이 바로 change of distance measurement, 즉 gauge change죠.) 실제로는 "measurement"하고 별 관계가 없기 때문에 제대로 된 용어라고는 할 수 없습니다만 (예를 들어 phase change가 더 적절합니다) 아무튼 이러한 역사적인 이유로 gauge theory라는 말이 생겨났습니다. |