Conserved currents of massless fields of spin s ≥ ½
Conserved currents of massless fields of spin s ≥ ½
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无质量自旋场的守恒流 s ≥ ½
DOI：
10.1098/rspa.2002.1070
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发表时间：
2002
期刊：
影响因子：
--
通讯作者：
J. Pohjanpelto
中科院分区：
文献类型：
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作者：
S. Anco;J. Pohjanpelto
对于四维平坦时空中任意自旋s ≤1/2的无质量线性对称旋量场，得到了所有局部构造的守恒流和相应的守恒张量的完整而明确的分类.这些结果推广了最近的分类在自旋s = 1的情况下，所有的保守电流局部构造的电磁旋量场。目前的分类产生了自旋s ≤1/2的类似物的著名的电磁应力-能量张量和Lipkin的zilch张量，以及自旋s ≤1/2的类似物的一个新的手征张量中发现的自旋s = 1的情况。手征张量在自旋-s场的对偶对称（即相位旋转）下具有奇宇称，而应力-能量和零张量则具有偶宇称。作为主要结果，我们证明了对于s ≤1/2，每个局部构造的守恒流都等价于初等线性守恒流、与应力-能量相关的二次守恒流、zilch张量和手征张量之和，以及这些电流的高阶导数扩展，其中自旋s场被替换为它关于平坦时空的共形Killing向量的重复共形加权李导数。此外，所有的电流有一个直接的统一的特征，在杀害旋量。s = 2、s = 1/2和s = 3/2的情况分别提供了引力子（即线性化的引力波）、中微子和引力子在平坦时空中传播的完整守恒量集。讨论了零量和手征量的物理意义。
A complete and explicit classification of all locally constructed conserved currents and underlying conserved tensors is obtained for massless linear symmetric spinor fields of any spin s ≤1/2 in four–dimensional flat spacetime. These results generalize the recent classification in the spin s = 1 case of all conserved currents locally constructed from the electromagnetic spinor field. The present classification yields spin s ≤1/2 analogues of the well–known electromagnetic stress–energy tensor and Lipkin's zilch tensor, as well as a spin s ≤1/2 analogue of a novel chiral tensor found in the spin s = 1 case. The chiral tensor possesses odd parity under a duality symmetry (i.e. a phase rotation) on the spin–s field, in contrast to the even parity of the stress–energy and zilch tensors. As a main result, it is shown that every locally constructed conserved current for each s ≤1/2 is equivalent to a sum of elementary linear conserved currents, quadratic conserved currents associated with the stress–energy, zilch and chiral tensors, and higher–derivative extensions of these currents in which the spin–s field is replaced by its repeated conformally weighted Lie derivatives with respect to conformal Killing vectors of flat spacetime. Moreover, all of the currents have a direct unified characterization in terms of Killing spinors. The cases s = 2, s = 1/2 and s = 3/2 provide a complete set of conserved quantities for propagation of gravitons (i.e. linearized gravity waves), neutrinos and gravitinos, respectively, on flat spacetime. The physical meaning of the zilch and chiral quantities is discussed.