J. Korean Math. Soc. 2001; 38(2): 275-281
Printed March 1, 2001
Copyright © The Korean Mathematical Society.
Takeyuki Hida
Meijo University
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
2001; 38(2): 349-363
2001; 38(2): 365-383
© 2022. The Korean Mathematical Society. Powered by INFOrang Co., Ltd