Dirac field in AdS2 and representations of SL̃(2,R).

We analyze a massive spinor field satisfying the Dirac equation in the universal covering space of two-dimensional anti-de Sitter space. In order to obtain well-defined dynamics for the classical field despite the lack of global-hyperbolicity of the spacetime, we impose a suitable set of boundary conditions that render the spatial component of the Dirac operator self-adjoint. Then, we find which of the solution spaces obtained by imposing the self-adjoint boundary conditions are invariant under the action of the isometry group of the spacetime manifold, namely, the universal covering group of S L (2 , R). The invariant solution spaces are then identified with unitary irreducible representations of this group using the classification given by Pukánszky [Math. Ann. 156, 96–143 (1964)]. We determine which of these correspond to invariant positive- or negative-frequency subspaces and, thus, result in a vacuum state invariant under the isometry group after canonical quantization. Additionally, we examine the invariant theories obtained from the self-adjoint boundary conditions, which result in a non-invariant vacuum state, identifying the unitary representation this state belongs to. [ABSTRACT FROM AUTHOR]