# Feynman integral over histories= over paths?

Gold Member
In computing the integral over past histories, does one restrict oneself to continuous paths, or does one take all possible combinations of points between the beginning and the end? If one sticks to the continuous paths, what justification is there in that?

Related Quantum Physics News on Phys.org

Continuous, perhaps even with some conditions on derivatives that should exist almost everywhere. See for instance Albeverio and Hogh-Krohn, "Mathematical Theory of Feynman Path Integrals".

Gold Member

Since I presently do not have access to a scientific library, and the book does not seem to be easily downloadable, and rather expensive to order, I cannot follow up on your book recommendation. If you have any recommendations from the Internet, I would be happy to follow them up.

For a starter you can check this: http://www.scholarpedia.org/article/Path_integral" [Broken], but there are several different approaches. The class of admissible paths depends on what you want to integrate. For instance you will find a sentence like this:

"This has the effect of restricting the integration to paths that satisfy a Hölder condition of order 3/2 and are thus differentiable, in such a way that expectations values with dq/dt are defined."

Last edited by a moderator:

Gold Member
Thank you, arkajad. Upon a first reading the link appears quite useful, and I shall be working through it.

#### lucid

For a starter you can check this: http://www.scholarpedia.org/article/Path_integral" [Broken], but there are several different approaches. The class of admissible paths depends on what you want to integrate. For instance you will find a sentence like this:

"This has the effect of restricting the integration to paths that satisfy a Hölder condition of order 3/2 and are thus differentiable, in such a way that expectations values with dq/dt are defined."
there is no reason paths have to be differentiable. in fact the stochastic approach to QM gives inherently non-differentiable paths.

a path which is not continuous would mean a particle that starts at some point and disappears into the vacuum an then reappears and then makes it out to some final endpoint.

the book Path Integral Methods in QFT by Rivers explains this stuff. it is easily downloadable.

Last edited by a moderator:

Gold Member

### Physics Forums Values

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving