Unique definition of the Zeeman-splitting g tensor of a Kramers doublet

It has been widely accepted in the past that the g tensor describing the Zeeman splitting of a Kramers doublet is not uniquely defined. Here we show that with two basic requirements, (i) the invariance, of the Zeeman Hamiltonian under symmetry transformations and (ii) its continuous change with the variations of the parameters of the system (geometry and crystal field), a unique determination of the elements of the g tensor is achieved.