标题： 度量Clifford代数 显示英文标题

标题： Metric Clifford Algebra

摘要： 本文中我们引入了度量Clifford代数的概念 $\mathcal{C\ell}(V,g)$，对于一个具有度量延拓子 $g$ 的 $n$-维实向量空间 $V$，其符号为 $(p,q)$，其中 $p+q=n$。 度量 Clifford 乘积在$\mathcal{C\ell}(V,g)$上表现为由$g$引导的\emph{变形}（在$\mathcal{C\ell}(V)$上的欧几里得 Clifford 乘积诱导而来）。 与度规外延 $g,$ 相关的还有一个规范度规外延 $h$，它编码了所有仅由 $g.$ 所包含的几何信息。这种 $h$ 的具体形式在这里被确定。 此外，我们提出了所谓的 \emph{黄金公式，} 并给出了证明，该内容在多元函数、微分几何和理论物理的研究中许多自然出现的应用中非常重要。 显示英文摘要

摘要： In this paper we introduce the concept of metric Clifford algebra $\mathcal{C\ell}(V,g)$ for a $n$-dimensional real vector space $V$ endowed with a metric extensor $g$ whose signature is $(p,q)$, with $p+q=n$. The metric Clifford product on $\mathcal{C\ell}(V,g)$ appears as a well-defined \emph{deformation}(induced by $g$) of an euclidean Clifford product on $\mathcal{C\ell}(V)$. Associated with the metric extensor $g,$ there is a gauge metric extensor $h$ which codifies all the geometric information just contained in $g.$ The precise form of such $h$ is here determined. Moreover, we present and give a proof of the so-called \emph{golden formula,} which is important in many applications that naturally appear in ours studies of multivector functions, and differential geometry and theoretical physics.