# Part I: Vector Analysis of Spinors

@article{Sobczyk2015PartIV, title={Part I: Vector Analysis of Spinors}, author={Garret Sobczyk}, journal={arXiv: Mathematical Physics}, year={2015} }

Part I: The geometric algebra G3 of space is derived by extending the real number system to include three mutually anticommuting square roots of +1. The resulting geometric algebra is isomorphic to the algebra of complex 2× 2 matrices, also known as the Pauli algebra. The so-called spinor algebra of C2, the language of the quantum mechanics, is formulated in terms of the idempotents and nilpotents of the geometric algebra G3, including its beautiful representation on the Riemann sphere, and a…

## 5 Citations

Part II: Spacetime Algebra of Dirac Spinors

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In "Part I: Vector Analysis of Spinors", the author studied the geometry of two component spinors as points on the Riemann sphere in the geometric algebra of three dimensional Euclidean space. Here,…

Spinors in Spacetime Algebra and Euclidean 4-Space

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This article explores the geometric algebra of Minkowski spacetime, and its relationship to the geometric algebra of Euclidean 4-space. Both of these geometric algebras are algebraically isomorphic…

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The real number system is geometrically extended to include three new anticommuting square roots of plus one, each such root representing the direction of a unit vector along the orthonormal…

Geometric Spinors, Relativity and the Hopf Fibration

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This article explores geometric number systems that are obtained by extending the real number system to include new anticommuting square roots of +1 or -1, each such new square root representing the…

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- 2018

Geometric algebra is the natural outgrowth of the concept of a vector and the addition of vectors. After reviewing the properties of the addition of vectors, a multiplication of vectors is introduced…

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