arXiv 1607.013162016-07hep-th

关于连续自旋粒子的规范理论的注记

Remarks on a Gauge Theory for Continuous Spin Particles

Victor O. Rivelles

备注：: 21 pages, typos corrected, improved presentation of section VI, final version
DOI：: 10.1140/epjc/s10052-017-4927-1

摘要：

本文系统地讨论了Schuster和Toro提出的连续自旋粒子的规范理论。我们表明，它是自然制定在一个余切丛闵可夫斯基时空的规范场依赖于时空坐标${x^μ}$和一个共向量$η_μ$。我们讨论了如何在$η_μ$中以不同的方式扩展字段，以及这些扩展如何相互关联。场方程有一个狄拉克δ函数的导数与$η$ -双曲面$η^2+1=0$的支持，我们展示了它如何限制规范场的动态的$η$ -双曲面。然后，我们表明，壳上的字段进行一个单一的不可约的庞加莱群的一个连续的自旋粒子的酉表示。我们还展示了如何场可以用来建立一组协变方程维格纳描述连续自旋粒子的单粒子态的波函数。最后，我们证明了连续自旋粒子与背景阿贝尔规范场的最小耦合是不可能的，并对与引力的耦合作了一些评论。

英文摘要：

We discuss in a systematic way the gauge theory for a continuous spin particle proposed by Schuster and Toro. We show that it is naturally formulated in a cotangent bundle over Minkowski spacetime where the gauge field depends on the spacetime coordinate ${x^μ}$ and on a covector $η_μ$. We discuss how fields can be expanded in $η_μ$ in different ways and how these expansions are related to each other. The field equation has a derivative of a Dirac delta function with support on the $η$-hyperboloid $η^2+1=0$ and we show how it restricts the dynamics of the gauge field to the $η$-hyperboloid. We then show that on-shell the field carries one single irreducible unitary representation of the Poincaré group for a continuous spin particle. We also show how the field can be used to build a set of covariant equations found by Wigner describing the wave function of one-particle states for a continuous spin particle. Finally we show that it is not possible to couple minimally a continuous spin particle to a background abelian gauge field, and make some comments about the coupling to gravity.

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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英文摘要：

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