A spinor representation is a representation of a Spin group, or infinitesimally of a Special orthogonal Lie algebra, constructed from a Clifford algebra. In even dimensions it can split into two chiral spinor representations.
An irreducible complex Clifford algebra module in even spacetime dimension has dimension and splits under the connected Spin group into two Weyl spinor modules of dimension . In odd dimension , an irreducible spinor still has dimension but has no Weyl splitting. Reality conditions depend on signature and are additional to these complex counts.
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The term "spin representation" is commonly used in the context of quantum mechanics and refers to a mathematical framework for describing the intrinsic angular momentum (spin) of quantum particles. Spin is a fundamental property of quantum particles like electrons, protons, neutrons, and other elementary and composite particles. ### Key Elements of Spin Representation: 1. **Quantum States**: Spin states are represented as vectors in a Hilbert space.