Jules Henri Poincare(1854~1912)是法國數學家 數學物理學家 哲學家
科學與假設(Science and Hypothesis)
與其說邏輯 直觀比較重要
Poincare lemma :
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Mathematics |
Physics |
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Principal fiber bundle |
Gauge space |
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G structure |
Gauge group(such as SU(2)) |
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Connection form |
Gauge potential (such as A) |
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Curvature form |
Field strength (such as E and B) |
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Local trivialzation |
Choice of gauge |
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Transition function |
Change of gauge |
Gabrie
Lugo的著作 Differential eometry in Physics是廣義相對論與量子場的規範理論的數學基礎
The book features numerous examples of beautiful curves and surfaces often reflected in nature,
plus more advanced computations of trajectory of particles in black holes.
Also embedded in the later chapters is a detailed description of the famous Dirac monopole and instantons.