  The Quantum Transfer Matrix method based on the Suzuki-Trotter formulation is
extended to dynamical problems. The auto-correlation functions of the
Transverse Ising chain are derived by this method. It is shown that the
Trotter-directional correlation function is interpreted as a Matsubara's
temperature Green function and that the auto-correlation function is given by
analytic continuation of the Green function. We propose the Trotter-directional
correlation function is a new measure of the quantum fluctuation and show how
it works well as a demonstration.
