Space-Time Algebra

Hestenes, David

doi:10.1007/978-3-319-18413-5

Cited by 301 publications

(345 citation statements)

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“…Moreover, spinor wave functions in the Pauli and Dirac theories are column matrices, so their relation to vectors was not obvious either. Perfect resolution of these issues turned out to be keys to creating the spacetime algebra in my book [19,20], but I had to complete an imperfect doctoral thesis before I could see how to do it.…”

Section: Genesis Of Spacetime Algebramentioning

confidence: 99%

The Genesis of Geometric Algebra: A Personal Retrospective

Hestenes

2016

Adv. Appl. Clifford Algebras

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Abstract. Even today mathematicians typically typecast Clifford Algebra as the "algebra of a quadratic form," with no awareness of its grander role in unifying geometry and algebra as envisaged by Clifford himself when he named it Geometric Algebra. It has been my privilege to pick up where Clifford left off-to serve, so to speak, as principal architect of Geometric Algebra and Calculus as a comprehensive mathematical language for physics, engineering and computer science. This is an account of my personal journey in discovering, revitalizing and extending Geometric Algebra, with emphasis on the origin and influence of my book Space-Time Algebra. I discuss guiding ideas, significant results and where they came from-with recollection of important events and people along the way. Lastly, I offer some lessons learned about life and science.

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Section: Genesis Of Spacetime Algebramentioning

confidence: 99%

The Genesis of Geometric Algebra: A Personal Retrospective

Hestenes

2016

Adv. Appl. Clifford Algebras

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“…It has been shown by Hestenes [2] and others, that using a Clifford vector algebra is a natural way of incorporating spin into quantum mechanics as an automatic consequence of the vector structure of space and momentum. The units are, significantly, isomorphic to those of Pauli matrices.…”

Section: An Algebra For the Rewrite Processmentioning

confidence: 99%

Nilpotent Quantum Mechanics: Analogs and Applications

Marcer

Rowlands

2017

Front. Phys.

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The most significant characteristic of nilpotent quantum mechanics is that the quantum system (fermion state) and its environment (vacuum) are, in mathematical terms, mirror images of each other. So a change in one automatically leads to corresponding changes in the other. We have used this characteristic as a model for self-organization, which has applications well beyond quantum physics. The nilpotent structure has also been identified as being constructed from two commutative vector spaces. This zero square-root construction has a number of identifiable characteristics which we can expect to find in systems where self-organization is dominant, and a case presented after the publication of a paper by us on "The 'Logic' of Self-Organizing Systems" [1], in the organization of the neurons in the visual cortex. We expect to find many more complex systems where our general principles, based, by analogy, on nilpotent quantum mechanics, will apply.

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“…For n > 2 an antiderivative is given by 6) where n(x) is the unit outward normal to ∂V . (The normal can be computed as n = I −1 I(x), where I is the pseudoscalar of G n and I(x) is the pseudoscalar of the tangent space to M at x.)…”

Section: ∇ Is Invertiblementioning

confidence: 99%

“…The American physicist and mathematician David Hestenes initiated the modern development of geometric algebra with the publication of Space-Time Algebra in 1966 [6]. He built on the work of Hamilton, Grassmann, and Clifford a century or so earlier.…”

Section: Introductionmentioning

confidence: 99%

A Survey of Geometric Algebra and Geometric Calculus

Macdonald

2016

Adv. Appl. Clifford Algebras

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This paper is an introduction to geometric algebra and geometric calculus, presented in the simplest way I could manage, without worrying too much about completeness or rigor. An understanding of linear algebra and vector calculus is presumed. This should be sufficient to read most of the paper."The principal argument for the adoption of geometric algebra is that it provides a single, simple mathematical framework which eliminates the plethora of diverse mathematical descriptions and techniques it would otherwise be necessary to learn." [15]

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Space-Time Algebra

Cited by 301 publications

References 0 publications

The Genesis of Geometric Algebra: A Personal Retrospective

The Genesis of Geometric Algebra: A Personal Retrospective

Nilpotent Quantum Mechanics: Analogs and Applications

A Survey of Geometric Algebra and Geometric Calculus

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