论文标题
$（k，n）$时空尺寸的外部代数多送货机的广义麦克斯韦方程
Generalized Maxwell equations for exterior-algebra multivectors in $(k,n)$ space-time dimensions
论文作者
论文摘要
本文将电磁场和源电流的外部代数概括为$ r $ $ r $和$ r-1 $的多元电流，分别是$ n $ space和$ k $ time dimensions。麦克斯韦方程的公式和洛伦兹的洛伦兹力量的$ r $，$ n $和$ k $的任意值以内部和外部衍生物的形式进行假定，其形式与其矢量量表类似物非常相似。这些公式从$ r-1 $级的潜力方面提供了解决方案，并以任何值的压力能量能量量为$ r $，$ n $和$ k $的压力能量量张量，为此提供了简单的明确公式。作为一种应用，根据电势的傅立叶变换，给出了$（n+k-1）$ - 尺寸时空切片的应力 - 能量弹药量的表达式。麦克斯韦方程与外部微积分的抽象结合了矢量演算的简单性和直觉，因为公式接纳了显式表达式，以及张量和差异形式的幂和差异形式，因为可以为任何$ r $，$ n $和$ k $的值提供公式。
This paper presents an exterior-algebra generalization of electromagnetic fields and source currents as multivectors of grades $r$ and $r-1$ respectively in a flat space-time with $n$ space and $k$ time dimensions. Formulas for the Maxwell equations and the Lorentz force for arbitrary values of $r$, $n$, and $k$ are postulated in terms of interior and exterior derivatives, in a form that closely resembles their vector-calculus analogues. These formulas lead to solutions in terms of potentials of grade $r-1$, and to conservation laws in terms of a stress-energy-momentum tensor of rank 2 for any values of $r$, $n$, and $k$, for which a simple explicit formula is given. As an application, an expression for the flux of the stress-energy-momentum tensor across an $(n+k-1)$-dimensional slice of space-time is given in terms of the Fourier transform of the potentials. The abstraction of Maxwell equations with exterior calculus combines the simplicity and intuitiveness of vector calculus, as the formulas admit explicit expressions, with the power of tensors and differential forms, as the formulas can be given for any values of $r$, $n$, and $k$.
