标题： 双曲轨道空间的Casimir能量与圆锥奇点 显示英文标题

标题： Casimir energy of hyperbolic orbifolds with conical singularities

摘要： 在本文中，我们通过使用zeta正则化技术，得到了二维Clifford-Klein空间形式的Casimir能量的显式表达式，该表达式基于底层时空的几何数据。时空被几何地表示为一个可能具有有限多个圆锥奇点的紧致双曲轨道面。在计算来自圆锥奇点的能量贡献时，我们推导出一个椭圆轨道积分的表达式，该表达式是一个特殊函数的无限和。我们证明了这个和以指数级速度收敛。此外，我们在对$(2, 3, 7)$-三角群轨道面的原始闭测地线长度增长的一个自然假设（已知在渐近情况下成立）下，证明了其Casimir能量是正的（排斥的）。 显示英文摘要

摘要： In this article, we obtain the explicit expression of the Casimir energy for 2-dimensional Clifford-Klein space forms in terms of the geometrical data of the underlying spacetime with the help of zeta-regularization techniques. The spacetime is geometrically expressed as a compact hyperbolic orbifold surface that may have finitely many conical singularities. In computing the contribution to the energy from a conical singularity, we derive an expression of an elliptic orbital integral as an infinite sum of special functions. We prove that this sum converges exponentially fast. Additionally, we show that under a natural assumption (known to hold asymptotically) on the growth of the lengths of primitive closed geodesics of the $(2, 3, 7)$-triangle group orbifold its Casimir energy is positive (repulsive).