We study bosonic quantum field theory on the double covering \(\widetilde{dS}_{2}\) of the two-dimensional de Sitter universe, identified to a coset space of the group \(\mathrm{SL}(2, {{\mathbb {R}}})\). The latter acts effectively on \(\widetilde{dS}_{2}\) and can be interpreted as it relativity group. The manifold is locally identical to the standard the Sitter spacetime \({dS}_2\); it is globally hyperbolic, geodesically complete and an inertial observer sees exactly the same bifurcate Killing horizons as in the standard one-sheeted case. The different global Lorentzian structure causes, however, drastic differences between the two models. We classify all the \(\mathrm{SL}(2, {{\mathbb {R}}})\)-invariant two-point functions and show that: (1) there is no Hawking–Gibbons temperature; (2) there is no covariant field theory solving the Klein–Gordon equation with mass less than 1/2R , i.e., the complementary fields go away.

我们在二维de Sitter宇宙的双覆盖\（\ widetilde {dS} _ {2} \）上研究了玻色子量子场论，该双覆盖\ { \ mathrm {SL}（2， {{\ mathbb {R}}}）\）。后者对\（\ widetilde {dS} _ {2} \）有效，并且可以解释为相对论组。流形在局部上与Sitter时空\（{dS} _2 \）的标准相同；它是全局双曲的，在测地学上是完整的，并且惯性观察者看到的分叉Killing视域与标准单页案例中的完全相同。然而，不同的全球洛伦兹结构导致两种模型之间的巨大差异。我们将所有\（\ mathrm {SL}（2，{{\ mathbb {R}}}）\）分类-不变的两点函数，并表明：（1）没有霍金-长臂猿的温度；（2）没有协变场理论解决质量小于1/2 R的Klein-Gordon方程，即互补场消失了。