论文标题
$ \ mathrm {ads} _2 $和$ \ widetilde {\ mathrm {sl}}}}的表示（2，\ mathbb {r}）$
Dirac field in $\mathrm{AdS}_2$ and representations of $\widetilde{\mathrm{SL}}(2,\mathbb{R})$
论文作者
论文摘要
我们研究了二维抗DE保姆空间的通用覆盖空间中大型纺纱场的狄拉克方程的解决方案。对于质量参数的某些值，我们施加了一组合适的边界条件，这些条件使狄拉克操作员自我接合的空间成分。然后，我们在理论的等轴测组下使用纺纱场的转换属性，即，$ \ mathrm {sl}的通用覆盖组（2，\ mathbb {r}）$，以确定该组下哪些自动化联合边界边界条件是不变的。我们使用Pukanzki给出的分类确定了该组具有单一不可约定表示的相应解空间，并确定其中哪个对应于不变的正和负频率子空间，因此在等轴测组下的真空状态中。最后，我们检查了以非不变真空状态导致不变理论并确定真空状态所属的单一表示的情况。
We study the solutions to the Dirac equation for the massive spinor field in the universal covering space of two-dimensional anti-de Sitter space. For certain values of the mass parameter, we impose a suitable set of boundary conditions which make the spatial component of the Dirac operator self-adjoint. Then, we use the transformation properties of the spinor field under the isometry group of the theory, namely, the universal covering group of $\mathrm{SL}(2,\mathbb{R})$, in order to determine which self-adjoint boundary conditions are invariant under this group. We identify the corresponding solution spaces with unitary irreducible representations of this group using the classification given by Pukanzki, and determine which of these correspond to invariant positive- and negative-frequency subspaces and, hence, in a vacuum state invariant under the isometry group. Finally, we examine the cases where the self-adjoint boundary condition leads to an invariant theory with non-invariant vacuum state and determine the unitary representation to which the vacuum state belongs.
