相关论文: Thomas-Wigner rotation via Clifford algebras
Gives an elementary exposition of the twisted group algebra rep- resentation of simple Clifford algebras
The purpose of this paper is to provide an elementary introduction to the qualitative and quantitative results of velocity combination in special relativity, including the Wigner rotation and Thomas precession. We utilize only the most…
We investigate the construction and properties of Clifford algebras by a similar manner as our previous construction of the octonions, namely as a twisting of group algebras of Z_2^n by a cocycle. Our approach is more general than the usual…
In this paper we find a Clifford algebra associated to generalized Fibonacci quaternions. In this way, we provide a nice algorithm to obtain a division quaternion algebra starting from a quaternion non-division algebra and vice-versa.
Exact and simple calculation of Thomas rotation and Thomas precessions along a circular world line is presented in an absolute (coordinate-free) formulation of special relativity. Besides the simplicity of calculations the absolute…
The geometric calculus based on Clifford algebra is a very useful tool for geometry and physics. It describes a geometric structure which is much richer than the ordinary geometry of spacetime. A Clifford manifold (C-space) consists not…
These are lecture notes for a course on the theory of Clifford algebras, with special emphasis on their wide range of applications in mathematics and physics. Clifford algebra is introduced both through a conventional tensor algebra…
Because of its apparent complexity, the discussion of Wigner rotation is usually reduced to the study of Thomas precession, which is too specific a case to allow a deep understanding of boost composition. However, by simple arguments and…
We derive a set of Clifford-algebraic formulas for two major nonlinear conformal transformations of the physical quantities related to Maxwell's equations. The superiority of these formulas over their vector-tensorial counterparts are…
This paper is an elaboration of an introductory talk given by the author at a workshop on Clifford algebras at Tennessee Technical University, in May 2002. We give an introduction to the basic concepts of Clifford analysis, including links…
CLIFFORD performs various computations in Grassmann and Clifford algebras. It can compute with quaternions, octonions, and matrices with entries in Cl(B) - the Clifford algebra of a vector space V endowed with an arbitrary bilinear form B.…
Some connections between quadratic forms over the field of two elements, Clifford algebras of quadratic forms over the real numbers, real graded division algebras, and twisted group algebras will be highlighted. This allows to revisit real…
See math-ph/0205036 for an expanded version.
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…
In this paper we derive a Heisenberg-type uncertainty principle for the continuous Clifford wavelet transform. A brief review of Clifford algebra/analysis, wavelet transform on $\mathbb{R}$ and Clifford-Fourier transform and their…
Using elementary geometric tools, we apply essentially the same methods to derive expressions for the rotation angle of the swing plane of Foucault's pendulum and the rotation angle of the spin of a relativistic particle moving in a…
Wigner rotations are transformations that affect spinning particles and cause the observable phenomenon of Thomas precession. Here we study these rotations for arbitrary symmetry groups with a semi-direct product structure. In particular we…
We suggest Clifford algebra as a useful simplifying language for present quantum dynamics. Clifford algebras arise from representations of the permutation groups as they arise from representations of the rotation groups. Aggregates using…
In this paper we further develop the method of quaternion typification of Clifford algebra elements suggested by the author in the previous paper. On the basis of new classification of Clifford algebra elements it is possible to reveal and…
This paper focuses on studying the Donoho-Stark's type uncertainty principle for the continuous Clifford wavelet transform. A brief review of Clifford algebra/analysis, Clifford wavelet transform and their properties is conducted. Next,…