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Clifford algebras are associative algebras constructed from quadratic forms on vector spaces. They can be viewed as generalizations of real numbers, complex numbers and quaternions. When constrained to real numbers, the algebra are often referred to as "geometric algebra" and has use in theoretical physics.
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2-dimensional spin 1/2 representation of Lorentz Lie Algebra
In Peskin & Schroeder section $3.2$ they begin by telling us that they want to construct spin $1/2$ representations of the Lorentz Lie algebra. One way to do that, they say, is to first find a represe …