Magnetic field correlation tensor in a Universe space with a multiply connected space section
In the case of a Universe with a multiply connected space section, the concept of statistical homogeneity and isotropy for vector fields is discussed. Considering a flat 3D torus as a basic example, we show that the correlation tensor of a statistically homogeneous and isotropic (locally) solenoidal vector field depends on a set of functions corresponding to the homotopic classes of geodesics connecting the points in which the tensor is calculated. In contrast, such tensor in a simply connected Universe depends on just one function.