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Spinor

In mathematics and physics, a spinor is a geometrical object constructed from a given vector space (2 component), used to introduce extra dimensions in unitary transformations. These allow for a projective representation of the rotation or spin group. Spinors can describe both bosons and fermions in complex and differential algebraic geometries, while tensors describe only bosons (particles of force exchange).

First applied to mathematical physics by Wolfgang Pauli in 1927 upon the introduction of spin matrices, Paul Dirac discovered the relativistic theory of electron spin in 1928 by showing the connection between spinors and the Lorentz [transformation] group.

The typical spinor is a Dirac spinor, an element of the fundamental representation of complexified Clifford algebra, into which the spin group's spin may be embedded. Because the spinors may be described in different real and operational geometries and as Lie groups in Lie algebras, the Dirac spinor representation is the only one that exists in all applicable dimensions.

Web Resources On Spinor

Spinor (Wikipedia)
Spinor (Wolfram MathWorld)
Spinors

Book Resources On Spinor

Spinors and Space-Time by Roger Penrose and Wolfgang Rindler
Clifford Algebras and Spinors by Pertti Lounesto
Geometric Algebra for Physicists by Chris Doran and Anthony Lasenby

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