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arXiv 1902.07211hep-thmath-phmath.MP
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纯自旋$3/2$无发散反对称张量旋量的无质量Rarita-Schwinger场

Massless Rarita-Schwinger field from a divergenceless anti-symmetric-tensor spinor of pure spin-$3/2$

James P. Edwards, Mariana Kirchbach

备注：
18 pages. Updated to journal version
发表信息：
International Journal of Modern Physics A Vol. 34, No. 11, 1950060 (2019)
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摘要：

我们构造了Rarita-Schwinger基矢量$U^μ$，它跨越无质量四矢量$ A^μ$的直积空间$U^μ:=A^μ\otimes u_M$，具有无质量的Majorana旋量$u_M$，以及相关的场强张量${\mathcal T}^{μν}:=p^μU^ν-p^νU^μ$。${\mathcal T}^{μν}$空间是可约的，包含纯自旋$3/2$ $\in (3/2,0)\oplus (0,3/2)$的一个无质量子空间.我们展示了如何挑选出后者在一个独特的方式采取行动${\mathcal T}^{μν}$与早期派生的动量独立的投影仪，${\mathcal P}^{(3/2,0)}$，正确地构建从卡西米尔运营商的代数$so(1,3)$的齐次洛伦兹群。以这种方式，它成为可能的描述不可约的无质量$(3/2,0)\oplus (0,3/2)$载波空间的反对称张量的第二次与马约拉纳旋量组件，定义为$\left[ w^{(3/2,0) }\right]^{μν}:=\left[{\mathcal P}^{(3/2,0)}\right]^{μν}\,\,_{γδ}{\mathcal T}^{γδ}$。结论是，$(3/2,0)\oplus (0,3/2)$双矢量旋量场对于$U^μ$规范场可以起到与电磁场强度张量$F_{μν}$相关联的双矢量$(1,0)\oplus (0,1)$对于麦克斯韦规范场$A_μ$所起的作用相同的作用。相应地，我们发现自由电磁场方程$p^μF_{μν}=0$被自由无质量Rarita-Schwinger场方程$p^μ\left[ w^{(3/2,0)}\right]_{μν}=0$所取代，并补充了附加条件$γ^μγ^ν\left[ w^{(3/2,0)}\right]_{μν} =0$，这是一个调用Majorana扇区的约束。

英文摘要：

We construct the Rarita-Schwinger basis vectors, $U^μ$, spanning the direct product space, $U^μ:=A^μ\otimes u_M$, of a massless four-vector, $ A^μ$, with massless Majorana spinors, $u_M$, together with the associated field-strength tensor, ${\mathcal T}^{μν}:=p^μU^ν-p^νU^μ$. The ${\mathcal T}^{μν}$ space is reducible and contains one massless subspace of a pure spin-$3/2$ $\in (3/2,0)\oplus (0,3/2)$. We show how to single out the latter in a unique way by acting on ${\mathcal T}^{μν}$ with an earlier derived momentum independent projector, ${\mathcal P}^{(3/2,0)}$, properly constructed from one of the Casimir operators of the algebra $so(1,3)$ of the homogeneous Lorentz group. In this way it becomes possible to describe the irreducible massless $(3/2,0)\oplus (0,3/2)$ carrier space by means of the anti-symmetric-tensor of second rank with Majorana spinor components, defined as $\left[ w^{(3/2,0) }\right]^{μν}:=\left[{\mathcal P}^{(3/2,0)}\right]^{μν}\,\,_{γδ}{\mathcal T}^{γδ}$. The conclusion is that the $(3/2,0)\oplus (0,3/2)$ bi-vector spinor field can play the same role with respect to a $U^μ$ gauge field as the bi-vector, $(1,0)\oplus (0,1)$, associated with the electromagnetic field-strength tensor, $F_{μν}$, plays for the Maxwell gauge field, $A_μ$. Correspondingly, we find the free electromagnetic field equation, $p^μF_{μν}=0$, is paralleled by the free massless Rarita-Schwinger field equation, $p^μ\left[ w^{(3/2,0)}\right]_{μν}=0$, supplemented by the additional condition, $γ^μγ^ν\left[ w^{(3/2,0)}\right]_{μν} =0$, a constraint that invokes the Majorana sector.

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。

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