自旋j> 1玻色子在秩为2j的广义张量-旋量基上的二阶微分方程
Second order differential equations for bosons with spin j > 1 and in the bases of general tensor-spinors of rank-2j
摘要：
自旋j> 1的玻色子可以在巴格曼-维格纳框架内的一种可能性中通过一个唯一的阶数为自旋两倍的微分方程来描述，然而已知这是不一致的，因为它允许非局部的、幽灵的和因果传播的解，所有这些问题都很难解决。另一种可能性由Fierz-Pauli框架提供，该框架基于更舒适地处理二阶Klein-Gordon方程，但需要补充一个辅助条件。虽然后者的形式主义避免了一些病态的高阶方程，它仍然困扰着一些不一致的（经典）解决方案的波前在电磁环境中的因果传播。我们在这里提出了一种替代上述两种方法，结合了它们的优点，同时避免了相关的困难。也就是说，我们提出了一个唯一的严格（j，0）+（0，j）表示特定的二阶微分方程，这是可导的拉格朗日和其解决方案不违反因果关系。所讨论的方程将其自身呈现为克莱因-戈登算子与洛伦兹不可约表示空间上的动量独立投影的乘积，该空间是由自旋-洛伦兹群的卡西米尔不变量之一构造的。所用的基础是秩为2j的一般张量旋量。
英文摘要：
A boson of spin-j>1 can be described in one of the possibilities within the Bargmann-Wigner framework by means of one sole differential equation of order twice the spin, which however is known to be inconsistent as it allows for non-local, ghost and acausally propagating solutions, all problems which are difficult to tackle. The other possibility is provided by the Fierz-Pauli framework which is based on the more comfortable to deal with second order Klein-Gordon equation, but it needs to be supplemented by an auxiliary condition. Although the latter formalism avoids some of the pathologies of the high-order equations, it still remains plagued by some inconsistencies such as the acausal propagation of the wave fronts of the (classical) solutions within an electromagnetic environment. We here suggest a method alternative to the above two that combines their advantages while avoiding the related difficulties. Namely, we suggest one sole strictly (j,0)+ (0,j) representation specific second order differential equation, which is derivable from a Lagrangian and whose solutions do not violate causality. The equation under discussion presents itself as the product of the Klein-Gordon operator with a momentum independent projector on Lorentz irreducible representation spaces constructed from one of the Casimir invariants of the spin-Lorentz group. The basis used is that of general tensor-spinors of rank-2j.
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