447
edits
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)
Revision as of 15:56, 24 July 2023
, 24 July 2023→Spinors and Cohomology
| Line 1,649: | Line 1,649: | ||
| desc = Differential Forms in Algebraic Topology by Raoul Bott and Loring Tu. | | desc = Differential Forms in Algebraic Topology by Raoul Bott and Loring Tu. | ||
}} | }} | ||
</div> | |||
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). | |||
</div> | |||
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 == | == Notes == | ||