标题： 椭圆伪球管中的真空电流 显示英文标题

标题： Vacuum currents in elliptic pseudosphere tubes

摘要： 我们研究了空间拓扑、曲率和磁通量对(2+1)维时空中带电标量场的真空期望值（VEV）电流密度的影响。 椭圆伪球体被考虑为一个精确可解的背景几何。 在沿紧致维度的周期性条件下的一般相位中，分离了哈达玛函数中的拓扑贡献。 提供了该方向上电流密度分量的两种等效表达式。 相应的VEV是磁通量的周期函数，周期等于磁通量子。 在平直时空极限下，我们恢复了具有平面角缺值的一般值的圆锥空间的结果。 在椭圆伪球体的原点附近，空间曲率对真空电流密度的影响较弱。 对于紧致维度长度的小值也是如此。 利用椭圆伪球体与具有平面角缺值的(2+1)维德西特时空之间的共形关系，我们确定了局部德西特时空的静态和双曲真空态中符合共形耦合的质量为零的标量场的电流密度。 显示英文摘要

摘要： We examine the effects of spatial topology, curvature, and magnetic flux on the vacuum expectation value (VEV) of the current density for a charged scalar field in (2+1)-dimensional spacetime. The elliptic pseudosphere is considered as an exactly solvable background geometry. The topological contribution is separated in the Hadamard function for general phases in the periodicity condition along the compact dimension. Two equivalent expressions are provided for the component of the current density in that direction. The corresponding VEV is a periodic function of the magnetic flux with a period equal to the flux quantum. In the flat spacetime limit, we recover the result for a conical space with a general value of the planar angle deficit. Near the origin of the elliptic pseudosphere, the effect of the spatial curvature on the vacuum current density is weak. The same applies for small values of the length of the compact dimension. Using the conformal relations between the elliptic pseudosphere and the (2+1)-dimensional de Sitter spacetime with a planar angle deficit, we determine the current densities for a conformally coupled massless scalar field in the static and hyperbolic vacuum states of locally de Sitter spacetime.