  Generalizing recent work on isotropic tensor fields in isotropic and achiral
condensed matter systems from two to arbitrary dimensions we address both
mathematical aspects assuming perfectly isotropic systems and applications
focusing on correlation functions of displacement and strain field components
in amorphous solids. Various general points are exemplified using simulated
polydisperse Lennard-Jones particles in two dimensions. It is shown that the
strain components in reciprocal space have essentially a complex
circularly-symmetric Gaussian distribution albeit weak non-Gaussianity effects
become visible for large wavenumbers q where also anisotropy effects become
relevant. The dynamical strain correlation functions are strongly non-monotonic
with respect to q with a minimum roughly at the breakdown of the continuum
limit.
