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Groups and representations
Groups and representations

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MATH 412: NOTE ON INFINITE-DIMENSIONAL VECTOR SPACES

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Math 231b Lecture 01 G. Quick 1. Lecture 1: Vector bundles We start
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1 8. CONSERVATION LAWS The general form of a conservation law

... quantity p + B 2 / 2 µ0 is the total pressure. The second contribution is called the magnetic pressure; the magnetic field resists compression, just like the fluid pressure. The tensor BB / µ0 is called the hoop stress. We will see that it resists shearing motions. The total energy is the sum of the ...
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Four-vector

In the theory of relativity, a four-vector or 4-vector is a vector in Minkowski space, a four-dimensional real vector space. It differs from a Euclidean vector in how its magnitude is determined. The transformations that preserve this magnitude are the Lorentz transformations, which include spatial rotations, boosts (a change by a constant velocity to another inertial reference frame), and temporal and spatial inversions. Regarded as a homogeneous space, the transformation group of Minkowski space is the Poincaré group, which adds to the Lorentz group the group of translations. The Lorentz group may be represented by 4×4 matrices.The article considers four-vectors in the context of special relativity. Although the concept of four-vectors also extends to general relativity, some of the results stated in this article require modification in general relativity.
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