With the help of Non-Equilibrium Thermo Field Dynamics, a unified framework of the canonical operator formalism for quantum stochastic differential equations is constructed where the stochastic Liouville equation and the Langevin equation are, respectively, equivalent to the Schrodinger equation and the Heisen-berg equation in quantum mechanics. It was found that there exist at least two attractive formulations; one is based on a non-Hermitian martingale (a realization of the conservation of probability), and the other on a Hermitian martingale (a realization of the conservation of norm of a wave function). In this paper, the structures of two formulations are investigated in a systematic manner by means of the difference of martingale operators.
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