Path Integral Formulation: Allowable Paths?

[LarryS]

In Feynman’s Path Integral formulation of QM, one starts by considering all possible paths between two fixed space-time events.

Question: Must the wave-length associated with each allowable path divide evenly into the spatial length of the path?

 

[Sonderval]

Perhaps I'm stupid right now, but as far as I can see there is no such thing as a wavelength in the path integral - you just integrate over the action. If you have a free particle and consider a path taken with constant velocity, the phase given by exp(iS) will rotate with constant rate - in this case you could define something like a "wavelength" as the distance between two points of equal phase, but there is no need for this phase to have the same value at the end as at the starting point.

 

[stevendaryl]

In Feynman’s Path Integral formulation of QM, one starts by considering all possible paths between two fixed space-time events.

Question: Must the wave-length associated with each allowable path divide evenly into the spatial length of the path?

No, Feynman's path integral considers all possible paths, where a path is just a function from time to position. He doesn't even restrict it to continuous functions, let alone functions with a definite wavelength.