Titlebook: Quantum Field Theory III: Gauge Theory; A Bridge between Mat Eberhard Zeidler Book 2011 Springer-Verlag Berlin Heidelberg 2011 elementary p

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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

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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

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Fierce

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

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,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

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态学

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

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978-3-662-50595-3Springer-Verlag Berlin Heidelberg 2011