重温多向量收缩，第二部分

IF 1.1 2区数学 Q2 MATHEMATICS, APPLIED

Advances in Applied Clifford Algebras Pub Date : 2024-10-19 DOI:10.1007/s00006-024-01358-3

André L. G. Mandolesi

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引用次数: 0

摘要

上一篇文章重新整理了多向量的收缩和星对偶理论，这里我们介绍一些应用。首先，我们通过方程（v \wedge M = 0）和（v \mathbin {\lrcorner }M=0）来研究与一般多向量 M 相关的内部和外部空间。然后，我们用它们来分析 M 的特殊分解、因式分解和 "雕刻"，定义广义等级，并得到新的简单性标准，包括一套简化的类似普吕克的关系。我们还讨论了收缩与超对称性的关系，并给出了多费米子创造和湮灭算子的超级互调器公式。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

Multivector Contractions Revisited, Part II

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Multivector Contractions Revisited, Part II

The theory of contractions of multivectors, and star duality, was reorganized in a previous article, and here we present some applications. First, we study inner and outer spaces associated to a general multivector M via the equations \(v \wedge M = 0\) and \(v \mathbin {\lrcorner }M=0\). They are then used to analyze special decompositions, factorizations and ‘carvings’ of M, to define generalized grades, and to obtain new simplicity criteria, including a reduced set of Plücker-like relations. We also discuss how contractions are related to supersymmetry, and give formulas for supercommutators of multi-fermion creation and annihilation operators.

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来源期刊

Advances in Applied Clifford Algebras 数学-物理：数学物理

CiteScore

2.20

自引率

13.30%

发文量

审稿时长

3 months

期刊介绍： Advances in Applied Clifford Algebras (AACA) publishes high-quality peer-reviewed research papers as well as expository and survey articles in the area of Clifford algebras and their applications to other branches of mathematics, physics, engineering, and related fields. The journal ensures rapid publication and is organized in six sections: Analysis, Differential Geometry and Dirac Operators, Mathematical Structures, Theoretical and Mathematical Physics, Applications, and Book Reviews.