# Some Applications of Clifford Algebra in Geometry

@article{Gu2020SomeAO, title={Some Applications of Clifford Algebra in Geometry}, author={Ying-Qiu Gu}, journal={Structure Topology and Symplectic Geometry}, year={2020} }

In this chapter, we provide some enlightening examples of the application of Clifford algebra in geometry, which show the concise representation, simple calculation, and profound insight of this algebra. The definition of Clifford algebra implies geometric concepts such as vector, length, angle, area, and volume and unifies the calculus of scalar, spinor, vector, and tensor, so that it is able to naturally describe all variables and calculus in geometry and physics. Clifford algebra unifies and…

## 3 Citations

Application of Clifford Algebra in Solving the Eigen Equations of Quantum Mechanics

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Clifford algebra is unified language and efficient tool for geometry and physics. In this paper, we introduce this algebra to derive the integrable conditions for Dirac and Pauli equations. This…

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In this note we construct explicit complex and real matrix representations for the generators of real Clifford algebra $C\ell_{p,q}$. The representation is based on Pauli matrices and has an elegant…

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## References

SHOWING 1-10 OF 50 REFERENCES

Space-Time Geometry and Some Applications of Clifford Algebra in Physics

- MathematicsAdvances in Applied Clifford Algebras
- 2018

In this paper, we provide some enlightening applications of Clifford algebra in physics. Directly taking the generators of Clifford algebra as tetrad of space-time, we redefine some concepts of field…

A Note on the Representation of Clifford Algebra

- Mathematics
- 2020

In this note we construct explicit complex and real matrix representations for the generators of real Clifford algebra $C\ell_{p,q}$. The representation is based on Pauli matrices and has an elegant…

Clifford Geometric Algebras in Multilinear Algebra and Non-Euclidean Geometries

- Mathematics
- 2004

Given a quadratic form on a vector space, the geometric algebra of the corresponding pseudo-euclidean space is defined in terms of a simple set of rules which characterizes the geometric product of…

Clifford Algebra, Lorentz Transformation and Unified Field Theory

- Mathematics
- 2018

According to a framework based on Clifford algebra $$C\ell (1,3)$$Cℓ(1,3), this paper gives a classification for elementary fields, and then derives their dynamical equations and transformation laws…

The Genesis of Geometric Algebra: A Personal Retrospective

- Mathematics
- 2017

This is an account of the author's personal journey in discovering, revitalizing and extending Geometric Algebra, with emphasis on the origin and influence of his book Space-Time Algebra.

Clifford algebras and their applications to Lie groups and spinors

- Mathematics
- 2017

In these lectures, we discuss some well-known facts about Clifford algebras: matrix representations, Cartan's periodicity of 8, double coverings of orthogonal groups by spin groups, Dirac equation in…

A covariant approach to geometry using geometric algebra

- Mathematics, Computer Science
- 2004

Using the mathematical framework of conformal geometric algebra – a 5-dimensional representation of 3-dimensional space – is shown to provide an elegant covariant approach to geometry, thus enabling us to deal simply with the projective and non-Euclidean cases.

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…

The algebraic theory of spinors and Clifford algebras

- Mathematics
- 1996

This volume is the first in a projected series devoted to the mathematical and philosophical works of the late Claude Chevalley. It covers the main contributions by the author to the theory of…