# The construction of spinors in geometric algebra

@article{Francis2005TheCO,
title={The construction of spinors in geometric algebra},
author={Matthew R. Francis and Arthur B. Kosowsky},
journal={Annals of Physics},
year={2005},
volume={317},
pages={383-409}
}
• Published 20 March 2004
• Mathematics
• Annals of Physics
24 Citations
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## References

SHOWING 1-10 OF 27 REFERENCES
Scalar products of spinors and an extension of Brauer-Wall groups
The automorphism groups of scalar products of spinors are determined. Spinors are considered as elements of minimal left ideals of Clifford algebras on quadratic modules, e.g., on orthogonal spaces.
Cli ord Algebras and the Classical Groups
The Clifford algebras of real quadratic forms and their complexifications are studied here in detail, and those parts which are immediately relevant to theoretical physics are seen in the proper
An Introduction to Spinors and Geometry with Applications in Physics
• Physics
• 1988
There is now a greater range of mathematics used in theoretical physics than ever. The aim of this book is to introduce theoretical physicists, of graduate student level upwards, to the methods of
States and operators in the spacetime algebra
• Physics
• 1993
The spacetime algebra (STA) is the natural, representation-free language for Dirac's theory of the electron. Conventional Pauli, Dirac, Weyl, and Majorana spinors are replaced by spacetime
Geometric Algebra for Physicists
• Mathematics, Physics
• 2003
Geometric algebra is a powerful mathematical language with applications across a range of subjects in physics and engineering. This book is a complete guide to the current state of the subject with
Clifford Algebras and Spinors
A historical review of spinors is given together with a construction of spinor spaces as minimal left ideals of Clifford algebras. Spinor spaces of euclidean spaces over reals have a natural linear
On the algebra of Dirac bispinor densities: Factorization and inversion theorems
The algebraic system formed by Dirac bispinor densities ρi≡ψΓiψ is discussed. The inverse problem—given a set of 16 real functions ρi, which satisfy the bispinor algebra, find the spinor ψ to which
Orthogonal and Symplectic Clifford Algebras: Spinor Structures
Orthogonal and Symplectic Geometries.- Tensor Algebras, Exterior Algebras and Symmetric Algebras.- Orthogonal Clifford Algebras.- The Clifford Groups, the Twisted Clifford Groups and Their
Lie-groups as Spin groups.
• Mathematics
• 1993
It is shown that every Lie algebra can be represented as a bivector algebra; hence every Lie group can be represented as a spin group. Thus, the computational power of geometric algebra is available
REAL SPINOR FIELDS.
The Dirac equation is expressed entirely in terms of geometrical quantities by providing a geometrical interpretation for the (−1)½ which appears explicitly in the Dirac equation. In the modification