Results 61 to 70 of about 263 (180)
Clifford Algebra with Mathematica [PDF]
, 2008 The Clifford algebra of a n-dimensional Euclidean vector space provides a general language comprising vectors, complex numbers, quaternions, Grassman algebra, Pauli and Dirac matrices. In this work, we present an introduction to the main ideas of Clifford algebra, with the main goal to develop a package for Clifford algebra calculations for the ...
Aragon-Camarasa, G. +3 more
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Clifford Algebras and Possible Kinematics
Symmetry, Integrability and Geometry: Methods and Applications, 2007 We review Bacry and Lévy-Leblond's work on possible kinematics as applied to 2-dimensional spacetimes, as well as the nine types of 2-dimensional Cayley-Klein geometries, illustrating how the Cayley-Klein geometries give homogeneous spacetimes for all ...
Alan S. McRae
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Representation of Integral Formulas for the Extended Quaternions on Clifford Analysis
MathematicsThis work addresses a significant gap in the existing literature by developing integral representation formulas for extended quaternion-valued functions within the framework of Clifford analysis. While classical Cauchy-type and Borel–Pompeiu formulas are
Ji Eun Kim
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Circles and Clifford Algebras [PDF]
Functional Analysis and Its Applications, 2004 Consider a smooth map from a neighborhood of the origin in a real vector space to a neighborhood of the origin in a Euclidean space. Suppose that this map takes all germs of lines passing through the origin to germs of Euclidean circles, or lines, or a point. We prove that under some simple additional assumptions this map takes all lines passing though
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Square Root of a Multivector of Clifford Algebras in 3D: A Game with Signs
MathematicsAn 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
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Clifford Algebras and Liquid Crystalline Fermions
Physical Review XWe 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 +8 more
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MathematicsThe 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 +2 more
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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 +1 more
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Representation of nuclear magnetic moments via a Clifford algebra formulation of Bohm's hidden variables. [PDF]
Sci Rep, 2022 Santilli RM, Sobczyk G.
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One-dimensional Quaternion Fourier Transform and Some Applications
Bulletin of Computational Applied Mathematics, 2021 The Fourier transform is a very useful tool in many areas. This transform has been defined in many contexts, as complex numbers, quaternions, and Clifford algebras.
Eusebio Ariza García +2 more
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