张量规范条件与张量场分解
Tensor gauge condition and tensor field decomposition
摘要：
我们讨论了将张量场分离为纯规范分量和规范不变分量的各种提议。这种张量场分解与从爱因斯坦的广义相对论中的度规张量中识别出真实引力自由度的努力密切相关。我们表明，作为一个向量场，张量场分解有确切的对应关系，并可以来自，规范固定的方法。然而，张量场的复杂性在于，存在无穷多个完全规范条件，这与矢量场的库仑规范的唯一性形成对比。我们对这些张量规范条件及其相应的张量场分解进行了广泛的探索，涉及数学结构、运动方程、非线性性质;并表明显然没有一个单一的选择在所有方面都是优越的。
英文摘要：
We discuss various proposals of separating a tensor field into pure-gauge and gauge-invariant components. Such tensor field decomposition is intimately related to the effort of identifying the real gravitational degrees of freedom out of the metric tensor in Einstein's general relativity. We show that, as for a vector field, the tensor field decomposition has exact correspondence to, and can be derived from, the gauge-fixing approach. The complication for the tensor field, however, is that there are infinitely many complete gauge conditions, in contrast to the uniqueness of Coulomb gauge for a vector field. We make an extensive exploration of these tensor gauge conditions and their corresponding tensor field decompositions, regarding mathematical structures, equations of motion, nonlinear properties; and show that apparently no single choice is superior in all aspects.
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