Results 101 to 110 of about 1,958 (231)

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

Structure of factor algebras and clifford algebra

Linear Algebra and its Applications, 1996
This paper is concerned with the generalized spectral decomposition or eigenprojector form of a linear operator over any field that is a splitting field of its minimal polynomial. A number system is constructed which is isomorphic to the factor ring \(\mathbb{C} [\lambda]/ \langle\psi \rangle\) for an arbitrary polynomial \(\psi\).
openaire   +2 more sources

Clifford Algebras and Liquid Crystalline Fermions

Physical Review X
We show that Clifford algebras provide a natural language to describe the physics of liquid crystal defects in 3D. This framework shows that most of these defects have fermionic nature, as the director field profile on a 2D cross section can ...
N. Johnson, L. C. Head, O. D. Lavrentovich, A. N. Morozov, G. Negro, E. Orlandini, C. A. Smith, G. M. Vasil, D. Marenduzzo   +8 more
doaj   +1 more source

Differential Structure Of The Hyperbolic Clifford Algebra

, 2015
This paper presents a thoughful review of: (a) the Clifford algebra (Formula presented.) of multivecfors which is naturally associated with a hyperbolic space HV ; (b) the study of the properties of the duality product of multivectors and multiforms; (c)
Notte-Cuello E.A., Rodrigues Jr. W.A.
core   +1 more source

CLIFFORD ALGEBRAS - NEW RESULTS

, 2018
The main purpose of this paper is to present some new results about Clifford Algebras : exponential, real structures, Cartan algebras... As they address different topics and the definitions in Clifford Algebras still differ from one author to another, it
Dutailly, Jean Claude
core  

$\mathbb{A}$-Differentiability over Associative Algebras

Mathematics
The unital associative algebra structure A on Rn allows for defining elementary functions and functions defined by convergent power series. For these, the usual derivative has a simple form even for higher-order derivatives, which allows us to have the A-
Julio Cesar Avila, Martín Eduardo Frías-Armenta, Elifalet López-González   +2 more
doaj   +1 more source

Representation of nuclear magnetic moments via a Clifford algebra formulation of Bohm's hidden variables. [PDF]

Sci Rep, 2022
Santilli RM, Sobczyk G.
europepmc   +1 more source

The mathematical physical meaning of the Rarita Schwinger equation factored by a weighted Dirac operator, Part I

Bulletin of Computational Applied Mathematics, 2021
In this article we give a tour through Physics to explain the meaning of the Rarita Schwinger equation and determine its relationship with the Clifford algebras. We also relate the proposed first operators of Rarita Schwinger with the recent operators of
Benjamín de Zayas, Carmen Judith Vanegas   +1 more
doaj  

Quaternion algebras and clifford algebras

, 1999
이 논문에서 우리는 가환체에 대한 4원수 대수들과 a graded algebra를 공부하고 quaternion algebras이 Brauer 군에서 위수가 2인 원소와 대응함을 증명한다. 우리는 1차와 마찬가지로 n차에 대응하는 Clifford algebras의 구조를 결정함으로써 정규 이차 공간의 Clifford algebra와 Brauer 군의 원소를 연관시킬 수 있다. 우리는 1장의 결과를 타원곡선들의 자기준동형환에 적용하여 [3]의 몇 연습
최희선
core  

An Introduction to Real Clifford Algebras and Their Classification

, 2012
Real Clifford algebras are associative, unital algebras that arise from a pairing of a finite-dimensional real vector space and an associated nondegenerate quadratic form.
Neilson, Christopher S.
core   +1 more source