Abstract:
We provide a necessary and sufficient condition on the coefficient matrices A,C for the diagonalizability of quadratic fields of the form, X=∑ni,j=1(Aija†ia†jˉAijaiaj+Cija†iaj), where the a's and a†'s are the generators of the multi-dimensional Schrödinger Lie algebra. We also consider the Fock vacuum characteristic function ⟨Φ,eisXΦ⟩, of X and study its factorizability/decomposability and how it relates to the commutativity of the simple quadratic components of X.