Grassmann-Clifford Geometric Algebras from a Universal Null Substrate

This paper introduces the Quadratic Space of Null Vectors (QSNV) as a foundational hybrid Grassmann-Clifford geometric algebra structure, offering great computational advantages by replacing matrix operations with an index arithmetic. At the core is a Zero Residue Factorization (ZRF), defining the geometric stability of the algebra. The famous Valley of Stability in nuclear physics closely mirrors the algebraic structure of the QSNV. This work provides the necessary algebraic prerequisites for deriving the Standard Model, a geometric alternative to the traditional Hilbert space formulation of quantum mechanics. An Appendix speculates that QSNV is a natural language to investigate that spacetime geometry is just a physical manifestation of triangular inequalities of quantum information on emergent null cones.

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Publication Details

Journal
SPIRE - Sciences Po Institutional REpository
Published
2026-01-01
DOI
https://doi.org/10.13140/rg.2.2.13404.04488
Primary Topic
Algebraic structures and combinatorial models
Type
article
Field-Weighted Citation Impact
0.00
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article

Grassmann-Clifford Geometric Algebras from a Universal Null Substrate

Jesús Cruz Guzmán, Garret Sobczyk, Bill Page
SPIRE - Sciences Po Institutional REpository
Algebraic structures and combinatorial models
article

Grassmann-Clifford Geometric Algebras from a Universal Null Substrate

Jesús Cruz Guzmán, Garret Sobczyk, Bill Page
article en

Abstract

This paper introduces the Quadratic Space of Null Vectors (QSNV) as a foundational hybrid Grassmann-Clifford geometric algebra structure, offering great computational advantages by replacing matrix operations with an index arithmetic. At the core is a Zero Residue Factorization (ZRF), defining the geometric stability of the algebra. The famous Valley of Stability in nuclear physics closely mirrors the algebraic structure of the QSNV. This work provides the necessary algebraic prerequisites for deriving the Standard Model, a geometric alternative to the traditional Hilbert space formulation of quantum mechanics. An Appendix speculates that QSNV is a natural language to investigate that spacetime geometry is just a physical manifestation of triangular inequalities of quantum information on emergent null cones.

SPIRE - Sciences Po Institutional REpository
Openalex Percentile: Top 89%
Algebraic structures and combinatorial models
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