To be used in future
 Section 5.8: Slits Up Chapter 5: Path Integrals Section 5.10: Time-ordered Perturbation Theory 

5.9 Brownian Motion

As have seen above, the formal definition of the path integral causes problems due to the “ ” in the action. One way we can get rid of it is by performing a Wick-rotation, . This turns Schrödinger’s equation into a diffusion equation, When ignoring the potential, this exactly describes Brownian motion. If we look at the motion of a particle from position Described by free particle motion; “jagged path”
 Section 5.8: Slits Up Chapter 5: Path Integrals Section 5.10: Time-ordered Perturbation Theory