Élie Cartan's and later Penrose's spinor calculus shows that the representation theory of the Lorentz group, not the affine group, is the operative constraint, and this constraint is manageable within generalized differential geometry.
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Penrose(as a historical figure in mathematical physics)
Roger Penrose, a British mathematician and physicist who invented spinor calculus—a mathematical tool for describing how objects spin and rotate in space.
Representation theory(as a branch of mathematics)
The study of how abstract mathematical structures (like groups) can be represented using simpler objects like matrices or numbers that follow the same rules.
Spinor calculus(as a mathematical tool used in physics)
A mathematical system for working with spinors, which are objects that describe how things spin and rotate; it's like a special language for talking about rotations in physics.
Élie Cartan(as a historical figure in mathematics and geometry)
A French mathematician (1869–1951) who developed new ways of understanding geometry and shapes using tools called differential forms, which became foundational for modern physics.