网络添麻烦
发表于 2025-3-25 04:20:33
Temperature Fields on the Euclidean Manifold ,,) as the temperature at the point . on .. We are given the smooth curve . on . with ..:=.(0). In terms of position vectors at the origin, we describe the curve . by the smooth vector function .=.(.),.∈ℝ. The derivative . is called the directional derivative of the temperature field . along the trajectory . at the point ...
Anthropoid
发表于 2025-3-25 10:28:43
Cocycles and Observers,ased on a few geometric axioms. For didactic reasons, we start with (i). The idea is to use bundle charts (product bundles) and to describe the change of bundle coordinates by a cocycle. In fact, the two approaches (i) and (ii) are equivalent to each other. In (ii), the cocycle corresponds to the transition maps between the bundle charts.
真
发表于 2025-3-25 12:12:16
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增长
发表于 2025-3-25 17:47:50
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JOG
发表于 2025-3-25 23:51:48
,The Noncommutative Yang–Mills ,(,)-Gauge Theory,d tr (.)=0. Further examples for the Lie group . are the Lie groups .(.),.(.),.(.,ℂ),.(.,ℂ), and .(3) with .=3. We will show how the .(1)-gauge theory from Chap. 13 has to be modified in the case of a noncommutative gauge group . (e.g., . with .=2,3,…).
Lamina
发表于 2025-3-26 04:04:39
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Harass
发表于 2025-3-26 06:42:58
Symmetry Breaking,defect of gauge theories could be cured in the 1960s by using the so-called Higgs mechanism which equips the gauge bosons with mass. This way, the ..-bosons and the ..-boson obtain their mass in the Standard Model of particle physics. Physicists speak of symmetry breaking (or loss of symmetry) for the following reason.
粉笔
发表于 2025-3-26 12:14:22
,Covector Fields and Cartan’s Exterior Differential – the Beauty of Differential Forms,icle physics). In particular, as we will show in Chap. 19, the language of differential forms shows that Maxwell’s theory of electromagnetism fits Einstein’s theory of special relativity, whereas the language of classical vector calculus conceals the relativistic invariance of the Maxwell equations.
frozen-shoulder
发表于 2025-3-26 16:33:40
Prologue,llow a strict logical route. This will be done later on. At this point, we are going to emphasize the basic ideas. It is our goal to show the reader how the methods of modern differential geometry work in the case of Einstein’s theory of general relativity, which describes the gravitational force in
遗忘
发表于 2025-3-26 17:47:52
The Euclidean Manifold ,,Here, .(.) denotes the position vector starting at the origin . at time . with the terminal point .(.)=.+.(.). Let ..(.) denote the space of all the position vectors starting at the point .. This is a real 3-dimensional Hilbert space equipped with the inner product 〈.|.〉.:=. and the norm . for all .