AI 中文总结
研究$dS_4$平面补丁上自由麦克斯韦场，通过体规范量子化及表示理论观点，取晚期极限识别出特定算子，引入不变内积，解释了相关离散系列表示及分解，还探讨了与三维共形自旋 - 1规范场的可能联系。
AI 中文摘要
我们研究了四维德西特时空（$dS_4$）平面补丁上的自由麦克斯韦场。回顾了其在邦奇 - 戴维斯真空中的体规范量子化，并通过研究单粒子态在无穷小德西特变换下的变换性质给出了表示理论观点。取晚期极限时，识别出两个标度维数为$\Delta = 1$（主导）和$\Delta = 2$（次主导）的晚期算子。引入了受共形场论启发的、在德西特群（$SO(4,1)$）下不变的内积。解释了与光子相关的$SO(4,1)$的酉离散系列表示如何由这两个算子提供，以及相应的离散系列表示如何分解为对应于两个螺旋度$+1$和$-1$的表示的直和。展望中，借鉴了最近关于$dS_4$高自旋引力微观描述的提议，研究了$\Delta = 1$晚期算子与三维共形自旋 - 1规范场的可能联系。
英文摘要
We study the free Maxwell field on the planar patch of four-dimensional de Sitter spacetime ($dS_4$). We review its bulk canonical quantization in the Bunch-Davies vacuum, and we give a representation-theoretic viewpoint by studying the transformation properties of single-particle states under infinitesimal dS transformations. By taking the late-time limit, we identify two late-time operators with scaling dimensions $Δ=1$ (leading) and $Δ=2$ (subleading). We introduce CFT-inspired inner products invariant under the dS group ($SO(4,1)$) for states created by late-time operators acting on the Bunch-Davies vacuum. We explain how the unitary discrete series representations of $SO(4,1)$ associated with the photon are furnished by both operators, in contrast with the Maxwell field on $AdS$ where the $Δ=1$ operator corresponds to a non-normalizable mode. We also explain how the corresponding discrete series representations of $SO(4,1)$ split into a direct sum of representations corresponding to two helicities $+1$ and $-1$. This is achieved by taking advantage of the dS invariance of the self-dual and anti-self-dual sectors of the photon field strength. In our outlook, we draw inspiration from a recent proposal for the microscopic description of $dS_4$ higher-spin gravity where conformal gauge fields in 3 dimensions play a central role, and we investigate a possible connection of the $Δ=1$ late-time operator with a conformal spin-1 gauge field in 3 dimensions.
Comments43 pages = 39 pages + references
