能量动量守恒和Lipkin零
Energy-momentum conservation and Lipkin's zilch
摘要：
如诺特定理所述，物理系统作用的任何可微对称性都有相应的守恒定律。利普金介绍了零值守恒定律。但相应的对称性还有待确定。在这里我们找到了一种确定这些对称性的方法，并通过直接计算来表达$n$维Minkowski时空中zilch张量与电流密度的关系。并将此方法推广到计算能量守恒-动量守恒对称性。最后，我们证明了在n=4的特殊情况下，我们的一般方程的光学手征减少到光学手征密度和光学手征流的连续性方程。
英文摘要：
As Noether's theorem states any differentiable symmetry of the action of a physical system has a corresponding conservation law. Lipkin introduced the conservation laws of zilches. But the corresponding symmetries are yet to be determined. Here we find a method to determine those symmetries and by direct calculations express the zilch tensor's relation to current-density for $n$-dimensional Minkowski space-time. Also, we extend this method to calculate symmetries of conservation of energy-momentum. Finally we show that in the special case of n=4, our general equation governing optical chirality reduces to the continuity equation of optical chirality density and optical chirality flow.
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