It is known that odd-dimensional de Sitter space acts as a transparent potential for free fields. Previous studies have explained this phenomena by relating de Sitter free field equations of motion to the time-independent Schrodinger equation with known transparent potentials. In this work we show that de Sitter's transparency is a consequence of an infinite set of "hidden" symmetries. These symmetries arise from an accidental symmetry for the zero-mode of matter fields, as well as the boost isometry of de Sitter space. For simplicity, we consider the case of massive Klein-Gordon theory. We show that the Noether charges associated with these hidden symmetries distinguish the two linearly-independent solutions of the free field wave equation in the asymptotic past and future of de Sitter. Conservation of these charges requires that the asymptotic behavior of any solution be identical, up to a constant phase, in the future and the past, which is the property of transparency. In the quantized theory, these charges act trivially on particle states belonging to the in/out vacuum Fock space. For particle states constructed from other vacua, the action of the charges generates particles. We comment on how these hidden symmetries may be present in interacting theories.

中文翻译：

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透明 de Sitter 空间的隐藏对称性

众所周知，奇维德西特空间充当自由场的透明势。先前的研究已经通过将德西特自由场运动方程与具有已知透明电位的与时间无关的薛定谔方程相关联来解释这种现象。在这项工作中，我们表明德西特的透明度是无限组“隐藏”对称性的结果。这些对称性源于物质场零模式的偶然对称性，以及德西特空间的增强等距。为简单起见，我们考虑大规模 Klein-Gordon 理论的情况。我们表明，与这些隐藏对称性相关的诺特电荷区分了德西特渐近过去和未来的自由场波动方程的两个线性独立解。这些电荷的守恒要求任何解的渐近行为在未来和过去是相同的，直到一个恒定的阶段，这是透明的属性。在量子化理论中，这些电荷对属于输入/输出真空 Fock 空间的粒子状态作用不大。对于由其他真空构造的粒子状态，电荷的作用会产生粒子。我们评论这些隐藏的对称性如何出现在相互作用的理论中。