General structure of correlation functions in stochastic quantization

We investigate the general structure of stationary correlation functions in stochastic quantization. On the basis of the (D+1)-dimensional field-theoretical formulation (operator formalism), we prove the fluctuation dissipation theorem which establishes a link between two types of correlation functions φφ and φπ, π being the conjugate field to φ. A specific structure of the self-energies to the correlation functions is clarified in (D+1)-dimensional momentum space, which, together with the fluctuation dissipation theorem, enables us to extract the fictitious time dependence of the correlation functions: The correlation length along the fictitious time is inversely proportional to p2+mphys2, mphys being the physical (pole) mass obtained in ordinary field theory.