平坦时空中对称应力-能量-动量张量的外代数推导
An exterior-algebraic derivation of the symmetric stress-energy-momentum tensor in flat space-time
摘要：
本文刻画了拉格朗日密度表示为两个多向量场点积的场的对称二秩应力-能量-动量张量。例如，在一个实施例中，标量场或规范场。张量是通过直接应用外部代数方法来处理作用于无穷小时空平移的不变性而导出的;这种直接推导避免了使用正则张量。张量分量和张量本身的公式推导出通用值的多向量等级$s$和时间和空间维度的数量，$k$和$n$，分别。一个简单的，坐标自由，封闭形式的表达式的内部衍生物（发散）的对称应力-能量-动量张量也得到：这个表达式提供了一个自然的推广的洛伦兹力，出现在电磁理论的背景下。本文还简要地讨论了本文导出的公式在广义电磁、Proca作用量、Yang-Mills场和共形不变性等情况下的应用。
英文摘要：
This paper characterizes the symmetric rank-2 stress-energy-momentum tensor associated with fields whose Lagrangian densities are expressed as the dot product of two multivector fields, e. g., scalar or gauge fields, in flat space-time. The tensor is derived by a direct application of exterior-algebraic methods to deal with the invariance of the action to infinitesimal space-time translations; this direct derivation avoids the use of the canonical tensor. Formulas for the tensor components and for the tensor itself are derived for generic values of the multivector grade $s$ and of the number of time and space dimensions, $k$ and $n$, respectively. A simple, coordinate-free, closed-form expression for the interior derivative (divergence) of the symmetric stress-energy-momentum tensor is also obtained: this expression provides a natural generalization of the Lorentz force that appears in the context of the electromagnetic theory. Applications of the formulas derived in this paper to the cases of generalized electromagnetism, Proca action, Yang-Mills fields and conformal invariance are briefly discussed.
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