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发表于 2025-3-26 22:31:15
The Lie Group ,(1) as a Paradigm in Harmonic Analysis and Geometry, Lie group .(1) defined by . equipped with the usual multiplication of complex numbers. Equivalently, . The set .(1) is a real one-dimensional manifold, namely, the unit circle. This manifold is called the group manifold of the Lie group .(1). In particular, a Lie group . is called compact iff . is
elastic
发表于 2025-3-27 02:52:26
Rotations, Quaternions, the Universal Covering Group, and the Electron Spin,844, one year after Hamilton’s discovery of quaternions. In the language of quaternions, Euler’s rotation formula (6.6) reads elegantly as . Here, the given quaternion . contains the information about the rotation angle . and the rotation axis vector . of length one. In particular, for the norm of t
仲裁者
发表于 2025-3-27 08:15:37
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Fierce
发表于 2025-3-27 10:41:14
Temperature Fields on the Euclidean Manifold ,,rectional derivative of a temperature field . on the Euclidean manifold .. To this end, let . be a smooth function. In terms of physics, we regard .(.) 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
catagen
发表于 2025-3-27 14:36:41
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冰河期
发表于 2025-3-27 21:00:13
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forthy
发表于 2025-3-28 01:37:31
,The Noncommutative Yang–Mills ,(,)-Gauge Theory,e reader should have the special case in mind where .=2 and . This gauge group was used by Yang and Mills in 1954. Recall that the Lie group .(2) consists of all the unitary (2×2)-matrices . with det (.)=1. The corresponding Lie algebra .(2) consists of all the complex (2×2)-matrices . with ..=−. an
座右铭
发表于 2025-3-28 05:20:34
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态学
发表于 2025-3-28 09:47:40
The Axiomatic Geometric Approach to Bundles,rder to prove further geometric properties of these manifolds (e.g., curvature or parallel transport), we use the fact that, by definition, these properties do not depend on the choice of local bundle coordinates. Therefore, we can pass to special bundle coordinates. This is the situation of product
变化
发表于 2025-3-28 11:05:07
978-3-662-50595-3Springer-Verlag Berlin Heidelberg 2011