Results 61 to 70 of about 245 (169)

Clifford-based spectral action and renormalization group analysis of the gauge couplings

European Physical Journal C: Particles and Fields, 2019
The Spectral Action Principle in noncommutative geometry derives the actions of the Standard Model and General Relativity (along with several other gravitational terms) by reconciling them in a geometric setting, and hence offers an explanation for their
Ufuk Aydemir
doaj   +1 more source

Cyclic cubic points on higher genus curves

Journal of the London Mathematical Society, Volume 112, Issue 3, September 2025.
Abstract The distribution of degree d$d$ points on curves is well understood, especially for low degrees. We refine this study to include information on the Galois group in the simplest interesting case: d=3$d = 3$. For curves of genus at least 5, we show cubic points with Galois group C3$C_3$ arise from well‐structured morphisms, along with providing ...
James Rawson
wiley   +1 more source

Square Root of a Multivector of Clifford Algebras in 3D: A Game with Signs

Mathematics
An algorithm is presented to extract the square root from a multivector (MV) in real Clifford algebras Clp,q, where n=p+q≤3, in radicals. It is shown that in Cl3,0, Cl1,2, and Cl0,3 algebras, there are up to four isolated square roots in a case of the ...
Arturas Acus, Adolfas Dargys
doaj   +1 more source

Introduction to Clifford's Geometric Algebra

, 2013
Geometric algebra was initiated by W.K. Clifford over 130 years ago. It unifies all branches of physics, and has found rich applications in robotics, signal processing, ray tracing, virtual reality, computer vision, vector field processing, tracking, geographic information systems and neural computing.
openaire   +2 more sources

A Study of LFT Embeddings in the Second Order Clifford Algebra Cl(R²,º)

IEEE Access
Knowledge graph embedding models represent entities as vectors in continuous spaces and their relations by geometric transformations, mainly translation, and rotation.
Kossi Amouzouvi, Sahar Vahdati, Bowen Song, Bernard O. Bainson, Nur A. Zarin Nishat, Jens Lehmann   +5 more
doaj   +1 more source

On the Continuity Equation in Space–Time Algebra: Multivector Waves, Energy–Momentum Vectors, Diffusion, and a Derivation of Maxwell Equations

Mathematics
Historically and to date, the continuity equation (C.E.) has served as a consistency criterion for the development of physical theories. In this paper, we study the C.E. employing the mathematical framework of space–time algebra (STA), showing how common
Manuel Beato Vásquez, Melvin Arias Polanco   +1 more
doaj   +1 more source

Hecke algebra representations within Clifford geometric algebras of multivectors [PDF]

Journal of Physics A: Mathematical and General, 1999
Summary: We introduce Clifford geometric algebras of multivectors which exhibit a bilinear form which is not necessarily symmetric. Looking at a subset of bi-vectors in \(Cl(\mathbf K^{2n},B)\), we prove that these elements provide a representation of the Hecke algebra \(H_{\mathbf K}(n+1,q)\) if the bilinear form \(B\) is chosen appropriately.
openaire   +2 more sources

Elastic Curves and Euler–Bernoulli Constrained Beams from the Perspective of Geometric Algebra

Mathematics
Elasticity is a well-established field within mathematical physics, yet new formulations can provide deeper insight and computational advantages. This study explores the geometry of two- and three-dimensional elastic curves using the formalism of ...
Dimiter Prodanov
doaj   +1 more source

Generalized Degenerate Clifford and Lipschitz Groups in Geometric Algebras

Advances in Applied Clifford Algebras
33 ...
Ekaterina Filimoshina, Dmitry Shirokov
openaire   +2 more sources

A representation of twistors within geometric (Clifford) algebra

, 2006
33 pages, 7 figures.
Arcaute, Elsa, Lasenby, Anthony, Doran, Chris   +2 more
openaire   +2 more sources