任意自旋作为洛伦兹张量或张量旋量的玻色子和费米子Weinberg-Joos（j，0）+（0，j）态及二阶理论
Bosonic and fermionic Weinberg-Joos (j,0)+ (0,j) states of arbitrary spins as Lorentz-tensors or tensor-spinors and second order theory
摘要：
本文提出了一种描述任意单自旋-j态按Lorentz代数的（j，0）+（0，j）载流子空间变换的一般方法，玻色子用Lorentz张量，费米子用张量旋量，二阶拉格朗日量.该方法可以避免繁琐的矩阵演算和更高的\partial^{2j}阶波动方程固有的温伯格-Joos方法。我们从可约洛伦兹张量（张量旋量）表示空间托管一个唯一的（j，0）+（0，j）不可约部门和设计有一个表示减少算法的基础上的一个卡西米尔不变的洛伦兹代数。这种算法允许我们将感兴趣的纯自旋j扇区与其余扇区整齐地分开，同时保留单独的洛伦兹指数和狄拉克指数。然而，洛伦兹不变量是动量无关的，并且不提供波动方程。真正的波动方程得到的条件下考虑满足克莱因-戈登方程的洛伦兹张量。在这样做的时候，人们总是得到波动方程和相关的拉格朗日量，它们是动量的二阶。具体地说，一个自旋为3/2的粒子变换为（3/2，0）+（0，3/2），在完全反对称的二阶洛伦兹张量-旋量的基础上，可以用二阶拉格朗日量来描述.此外，粒子的传播因果关系内的电磁背景。在我们对（3/2，0）+（0，3/2）作为π_[μν]的一部分的研究中，我们再现了从温伯格-乔斯理论中已知的电磁多极矩。我们还发现了一个康普顿微分截面，满足幺正性的前进方向。所建议的张量演算相对于符号软件FeynCalc来说非常计算机友好。
英文摘要：
We propose a general method for the description of arbitrary single spin-j states transforming according to (j,0)+(0,j) carrier spaces of the Lorentz algebra in terms of Lorentz-tensors for bosons, and tensor-spinors for fermions, and by means of second order Lagrangians. The method allows to avoid the cumbersome matrix calculus and higher \partial^{2j} order wave equations inherent to the Weinberg-Joos approach. We start with reducible Lorentz-tensor (tensor-spinor) representation spaces hosting one sole (j,0)+(0,j) irreducible sector and design there a representation reduction algorithm based on one of the Casimir invariants of the Lorentz algebra. This algorithm allows us to separate neatly the pure spin-j sector of interest from the rest, while preserving the separate Lorentz- and Dirac indexes. However, the Lorentz invariants are momentum independent and do not provide wave equations. Genuine wave equations are obtained by conditioning the Lorentz-tensors under consideration to satisfy the Klein-Gordon equation. In so doing, one always ends up with wave equations and associated Lagrangians that are second order in the momenta. Specifically, a spin-3/2 particle transforming as (3/2,0)+ (0,3/2) is comfortably described by a second order Lagrangian in the basis of the totally antisymmetric Lorentz tensor-spinor of second rank, Ψ_[ μν]. Moreover, the particle is shown to propagate causally within an electromagnetic background. In our study of (3/2,0)+(0,3/2) as part of Ψ_[μν] we reproduce the electromagnetic multipole moments known from the Weinberg-Joos theory. We also find a Compton differential cross section that satisfies unitarity in forward direction. The suggested tensor calculus presents itself very computer friendly with respect to the symbolic software FeynCalc.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
