Coherent state representation for generalized bosonic Bogolyubov transformation

We show that the generalized bosonic Bogolyubov transformation generator U(G) = exp[1/2(a(i)G(ij)a(j)-a(i)(t)G(ij)(t)a(i)(t))] where G is a n x n matrix, has the manifest coherent state representation U(G) = (det cosh H)(1/2) integral Pi(i) [d(2)z(i)/pi] \z(j)(cosh H)(ji)-z(j)*(e(-lF)sinh H)(ji)][z(i)\, G = He-iF, This expression has the advantage of exhibiting the transition from classical transformation to its quantum mechanical correspondence apparent and providing us with a convenient approach for calculating some Bogolyubov transformed states.