标题： 具有螺旋紧致维度模型中的拓扑卡西米尔效应 显示英文标题

标题： Topological Casimir effect in models with helical compact dimensions

摘要： 我们研究了空间维度螺旋紧致化对具有通用曲率耦合参数的带电标量场真空态局域性质的影响。考虑了一个具有旋转对称性的广义背景几何，其中包含了出现在螺旋周期性条件中的坐标。结果表明，通过坐标变换，该问题可以简化为在同一局域几何中具有标准准周期性条件的问题，并且有效紧致半径由紧致维度的长度和螺旋参数决定。作为一般方法的应用，我们考虑了具有螺旋紧致维度的局部de Sitter时空。利用Bunch-Davies真空态的Hadamard函数，研究了场平方、电流密度以及能量-动量张量的真空期望值。拓扑贡献被明确分离，并在宇宙膨胀的早期和晚期阶段描述了它们的渐近行为。与准周期性条件问题相比的一个重要区别是，能量-动量张量的非对角分量和沿未紧致维度的电流密度分量出现非零值。 显示英文摘要

摘要： We investigate the influence of the helical compactification of spatial dimension on the local properties of the vacuum state for a charged scalar field with general curvature coupling parameter. A general background geometry is considered with rotational symmetry in the subspace with the coordinates appearing in the helical periodicity condition. It is shown that by a coordinate transformation the problem is reduced to the problem with standard quasiperiodicity condition in the same local geometry and with the effective compactification radius determined by the length of the compact dimension and the helicity parameter. As an application of the general procedure we have considered locally de Sitter spacetime with a helical compact dimension. By using the Hadamard function for the Bunch-Davies vacuum state, the vacuum expectation values of the field squared, current density, and energy-momentum tensor are studied. The topological contributions are explicitly separated and their asymptotics are described at early and late stages of cosmological expansion. An important difference, compared to the problem with quasiperiodic conditions, is the appearance of the nonzero off-diagonal component of the energy-momentum tensor and of the component of the current density along the uncompact dimension.