A spinor is a mathematical object used in physics, particularly in the fields of quantum mechanics and the theory of relativity. It is a type of vector that behaves differently than ordinary vectors under rotations and transformations. Specifically, spinors are essential in describing the intrinsic angular momentum (spin) of particles, such as electrons.
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A spinor is an element of a representation space for a Spin group; algebraically, spinor spaces arise from irreducible representations of a Clifford algebra or its even part. The Spin group is a double cover of a rotation group, so its action can distinguish rotations that ordinary vectors cannot.
For rotations in three-dimensional Euclidean space, a spinor can be a column in , acted on by . A rotation through angle about a unit direction acts as , where are the Pauli matrices. At this is , and at it is . The sign change explains the distinction between spinors and spatial vectors and underlies the representation of spin one-half. A spinor is not a literal square root of a vector; the relationship is through the Clifford algebra action.
- Physics from Symmetry by Jakob Schwichtenberg (2015) page 72
- physics.stackexchange.com/questions/172385/what-is-a-spinor
- physics.stackexchange.com/questions/41211/what-is-the-difference-between-a-spinor-and-a-vector-or-a-tensor
- physics.stackexchange.com/questions/74682/introduction-to-spinors-in-physics-and-their-relation-to-representations
- www.weylmann.com/spinor.pdf