| Summary: | 碩士 === 國立臺南大學 === 應用數學研究所碩士班 === 99 === In this research, we show how to use mathematical tools in physics. The main contents of this study are applications of mathematics for modern physics. The elds of physics
being showed are elementary particle, special and general relativity theory, and a little of electrodynamics.
In order to get what we want to do, we need group theory which is a portion of algebra. In this branch, we almost use continuous group which let us have an obvious expression of Lie algebra playing a very important role in the development of modern physics. In particular, it is the development of fundamental particle whose father is Gell|Mann and some of other physicists, they used abstract algebra as foundation for their theories. Another branch of mathematics being used is Geometry|theory of manifold with the notions of tangent vectors, tangent elds, tensor, etc... This theory gives formula for all physics''
laws which does not depend on coordinate system|general covariant principle. Mathematician and theoretical physicist have tried to unify Lorentz geometry and Riemann
geometry become semi{riemannian geometry. We only study semi{riemannian geometry and will not display those two geometries.
Through this study, it shows a general understanding of physics for students who are not physics'' student. Because, nowadays, modern physics is waiting for proving existence and uniffication by mathematics.
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