Super-energy tensors
Super-energy tensors
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超能张量
DOI：
10.1088/0264-9381/17/14/313
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发表时间：
1999
影响因子：
3.5
通讯作者：
J. Senovilla
中科院分区：
文献类型：
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作者：
J. Senovilla
任意维度的任意场超能（s-e）张量的简单且纯代数的构造都可以呈现。这些张量具有良好的数学和物理特性，并且它们可以用于任何以具有洛伦兹签名度量的 n 维流形作为基本领域的理论。一般来说，这些 s-e 张量的完全类时分量具有能量密度的数学特征：它们是正定的并满足主导属性，这提供了对全局结果有用的 s-e 估计，并有助于其他问题，例如场的因果传播。类似地，超动量矢量也具有 s-e 通量矢量的数学特性。引力场的经典贝尔和贝尔罗宾逊张量包含在我们的一般定义中。还获得了物理场的能量动量和超能张量，并且将通过在标量场、电磁场和普罗卡场的情况下明确地写出这些张量来说明该过程。此外，高阶（超）k 能量张量被定义并被证明是有意义的并且对于不同的物理场是一致的。在平坦时空中，它们提供了无限多个守恒量。在非平坦时空中，不同场之间s-e量交换的基本问题得到了解决，并得到了肯定的回答。只要存在杀伤矢量，任何最小耦合标量场都会发现守恒的 s-e 电流。此外，通过研究不连续性的传播还显示了引力和电磁超能的交换。这似乎为新型守恒定律物理定律打开了大门。
A simple and purely algebraic construction of super-energy (s-e) tensors for arbitrary fields is presented in any dimensions. These tensors have good mathematical and physical properties, and they can be used in any theory having as basic arena an n-dimensional manifold with a metric of Lorentzian signature. In general, the completely timelike component of these s-e tensors has the mathematical features of an energy density: they are positive definite and satisfy the dominant property, which provides s-e estimates useful for global results and helpful in other matters, such as the causal propagation of the fields. Similarly, super-momentum vectors appear with the mathematical properties of s-e flux vectors. The classical Bel and Bel-Robinson tensors for the gravitational fields are included in our general definition. The energy-momentum and super-energy tensors of physical fields are also obtained, and the procedure will be illustrated by writing down these tensors explicitly for the cases of scalar, electromagnetic, and Proca fields. Moreover, higher order (super)k-energy tensors are defined and shown to be meaningful and in agreement for the different physical fields. In flat spacetimes, they provide infinitely many conserved quantities. In non-flat spacetimes, the fundamental question of the interchange of s-e quantities between different fields is addressed, and answered affirmatively. Conserved s-e currents are found for any minimally coupled scalar field whenever there is a Killing vector. Furthermore, the exchange of gravitational and electromagnetic super-energy is also shown by studying the propagation of discontinuities. This seems to open the door for new types of conservation physical laws.