20: Sir Roger Penrose - Plotting the Twist of Einstein’s Legacy: Difference between revisions

20: Sir Roger Penrose - Plotting the Twist of Einstein’s Legacy (edit)

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 Spinors have two main instantiations: the infinitesimal quantity usually in finite dimensions as the value of a vector field at a point, or as the vector field taken over a finite region of space(time).
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-In finite dimensions, spinors are constructed via an algebraic means known as representation theory. The key fact that supports the construction is that the Lie groups of rotations <math> SO(n,\mathbb{R}) </math> acting on linear n-dimensional space admit double coverings <math> Spin(n) </math> such that two elements of the spin group correspond to a single rotation.
+For the infinitesimal quantity in finite dimensions, spinors are constructed via an algebraic means known as representation theory. The key fact that supports the construction is that the Lie groups of rotations <math> SO(n,\mathbb{R}) </math> acting on linear n-dimensional space admit double coverings <math> Spin(n) </math> such that two elements of the spin group correspond to a single rotation.
 == Notes ==