منابع مشابه
Clifford Algebra with Mathematica
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 computer algebra program Mathematica∗. The Cliffor...
متن کاملOn Computational Complexity of Clifford Algebra
After a brief discussion of the computational complexity of Clifford algebras, we present a new basis for even Clifford algebra Cl 2m that simplifies greatly the actual calculations and, without resorting to the conventional matrix isomorphism formulation, obtains the same complexity. In the last part we apply these results to the Clifford algebra formulation of the NP-complete problem of the m...
متن کاملGravitoelectromagnetism in a complex Clifford algebra
A linear vector model of gravitation is introduced in the context of quantum physics as a generalization of electromagnetism. The gravitoelectromagnetic gauge symmetry corresponds to a hyperbolic unitary extension of the usual complex phase symmetry of electromagnetism. The reversed sign for the gravitational coupling is obtained by means of the pseudoscalar of the underlying complex Clifford a...
متن کاملClifford algebra as quantum language
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 such representations for their permutations obey Clifford statistics. The vectors supporting the Clifford algebras of permutations and rotations are plexors an...
متن کاملGosset’s Figure in a Clifford Algebra
This note describes a way to realize a “projective” version of Gosset’s 240-vertex semiregular polytope 421 using the Clifford algebra Cl(8) generated by an 8-dimensional vector space equipped with a non-degenerate quadratic form. The 120 vertices of this projective Gosset figure are also seen to coincide with a particular basis for the Lie algebra so(16).
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ژورنال
عنوان ژورنال: Complex Variables and Elliptic Equations
سال: 2008
ISSN: 1747-6933,1747-6941
DOI: 10.1080/17476930701778869