Journal of the
Korean Mathematical Society JKMS

The trajectory of a classical dynamics is detrmined by the least action principle. As soon as we come to quantum dynamics, we have to consider all possible trajectories which are proposed to be a sum of the classical trajectory and Brownian fluctuation. Thus, the action involves the square of the derivative $\dot B(t)$ (white noise) of a Brownian motion $B(t)$ . The square is a typical example of a generalized white noise functional. The Feynman propagator should therefore be an average of a certain generalized white noise functional. This idea can be applied to a large class of dynamics with various kinds of Lagrangians.

Keywords: path integral, Feynman functional, generalized white noise functional(Hida distribution)

MSC numbers: Primary: 60H40, Secondary: 60G15, 81S40