A spinor is a vector in an irreducible module for a Clifford algebra or its even subalgebra,
with the induced group representation of
the corresponding spin group. In four-dimensional Minkowski space, the familiar Weyl spinors are two-component
complex column vectors
(Woit 2017, Chs. 31 and 41). For 
with 
, a full 
rotation in a Euclidean
plane changes the sign of a spinor. A tensor representation
of the corresponding orthogonal group is unchanged
(Woit 2017, Chs. 29 and 31).
Spinor
See also
Clifford Algebra, Minkowski Space, Spin Group, Spinor Field, Spinor Lie Derivative, Tensor, TwistorExplore with Wolfram|Alpha
References
Cartan, È. The Theory of Spinors. New York: Dover, 1981.Corson, E. M. Introduction to Tensors, Spinors and Relativistic Wave-Equations. London, England: Blackie and Son, 1955.Lounesto, P. "Counterexamples to Theorems Published and Proved in Recent Literature on Clifford Algebras, Spinors, Spin Groups, and the Exterior Algebra." http://www.hit.fi/~lounesto/counterexamples.htm.Misner, C. W.; Thorne, K. S.; and Wheeler, J. A. "Spinors." Ch. 41 in Gravitation. San Francisco, CA: W. H. Freeman, pp. 1135-1165, 1973.Morse, P. M. and Feshbach, H. "The Lorentz Transformation, Four-Vectors, Spinors." §1.7 in Methods of Theoretical Physics, Part I. New York: McGraw-Hill, pp. 93-107, 1953.Penrose, R. and Rindler, W. Spinors and Space-Time, Vol. 1: Two-Spinor Calculus and Relativistic Fields. Cambridge, England: Cambridge University Press, 1987.Penrose, R. and Rindler, W. Spinors and Space-Time, Vol. 2: Spinor and Twistor Methods in Space-Time Geometry. Cambridge, England: Cambridge University Press, 1987.Woit, P. Quantum Theory, Groups and Representations: An Introduction. Cham, Switzerland: Springer, 2017. https://www.math.columbia.edu/~woit/QMbook/qmbook-latest.pdf.Referenced on Wolfram|Alpha
SpinorCite this as:
Weisstein, Eric W. "Spinor." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/Spinor.html