Fourier transform for replicated systems

Replica trick turns out to be a powerful method to deal with disordered systems. Nevertheless, if several replicas are involved, calculations become technically difficult in the presence of a spontaneous symmetry breaking. Given a Parisi Replica Symmetry Breaking (RSB) scheme, the Fourier Transform on the replica group (RFT) has the same properties of the usual Fourier transform and in particular the convolution products in the replica space are immediately “diagonalized” in the Fourier space.