Let
be a real
finite-dimensional vector space. We introduce some physical problems that may be described by
-valued homogeneous and
isotropic random fields on
.
We propose a general method for calculation of expectations and two-point correlation
functions of such fields. Our results are equivalent to classical results by Robertson, when
, and those by
Lomakin, when
is the space of symmetric second-rank tensors over
. Our
solution involves an analogue of the classical Clebsch–Gordan coefficients.
Keywords
isotropic tensor random field, group representation,
Godunov–Gordienko coefficients