Physical interpretation of Feynman path integral

[Feynman]

Hi
What is the physical interpretation of Feynman path integral?
Thanks

 

[marcus]

Hi
What is the physical interpretation of Feynman path integral?
Thanks

here is one view: it does not have a physical interpretation
because it is a way of calculating a sometimes very close approximation

but nature does not know or care how we calculate
she does something, we don't know exactly how
and we have this way of calculating that gets the right answer

it's like virtual particles---maybe they don't exist in nature but they are good to calculate with

it's like feynmann diagrams: maybe nature doesn't know about them---she doesn't need to because she has her own way of doing things without perturbation series----maybe nothing in nature corresponds to feynmann diagrams---they are useful, tho, for organizing the calculation of a perturbation expansion.

that is just one viewpoint
hopefully someone else will provide a contrasting one

BTW Feynmann, if you haven't already I invite you to have a look in this Quantum Physics forum
at the electroweak conversation between turin and zephram.
if zephram answers on this thread it will probably be interesting

 

[Feynman]

But I know that the path integral have a physical interpretation but i don't know

 

[meldi]

hello marcus!
I'm interested by the subject but I didn't find the post of turin and zephram. Can you give me a link please?

 

[JohnDubYa]

Read Feynman and Hibbs' book "Path Integrals." The introduction should satisfy your curiosity.

 

[Feynman]

So i don't have the Feynman Hibbs book
So can u tell me about the physical interpretation of the path integrals :@

 

[Olias]

It relational to the many 'sum-over-history' interpretation also by Feynman.
For instance:The fundamental question in the path integral (PI) formulation of quantum mechanics is:If the particle is at a position q at time t = 0, what is the probability amplitude that it will be at some other position q0 at a later time t = T?

This I took from this good paper:http://arxiv.org/PS_cache/quant-ph/pdf/0004/0004090.pdf

If you read through it, you can form your own viewpoint, interpretation is open to a vast number of probibilities, every path has many (integral-able)(connecting) histories!

PS the original paper by Feynman was rejected!

 

[somy]

Dear Olias;
I see the link. can you tell me how did dirac observed the action plays a central role?
(also the difference between lagrangian and hamiltonian interpretation)
Tanks in advanced.

 

[robphy]

You might want to start off reading some of these introductory articles by EF Taylor
http://www.eftaylor.com/leastaction.html
and watching some of Feynman's lectures in Auckland (which became "QED")
http://www.vega.org.uk/series/lectures/feynman/

 

[Feynman]

But I think taht the Feynman path integral is a link between the quantum physics and the quantum field theory, but how?

 

[marcus]

hello marcus!
I'm interested by the subject but I didn't find the post of turin and zephram. Can you give me a link please?

hi meldi, sorry I didnt respond earlier, I will get a link to that
electroweak thread in the Quantum Physics forum

here's the part of my post that I think you are responding to:

...BTW Feynmann, if you haven't already I invite you to have a look in this Quantum Physics forum
at the electroweak conversation between turin and zephram.
if zephram answers on this thread it will probably be interesting...

the thread begins here:
https://www.physicsforums.com/showthread.php?t=31857

first Duct Taper says something
then Zephram replies
then Turin says "I would like to hear a little more..."

it is really turins perceptive questioning that elicits the good exposition
that thread is a model of what I wish we had more of

 

[dlgoff]

...that thread is a model of what I wish we had more of

Yes indeed. I followed that thread and was fascinated by zephram. Thanks zephram.

Regards

 

[JohnDubYa]

RE: "So i don't have the Feynman Hibbs book "

Then buy it, or check it out from the library.

 

[meldi]

thank you very much Marcus!

 

[selfAdjoint]

RE: "So i don't have the Feynman Hibbs book "

Then buy it, or check it out from the library.

I bought Feynman Hibbs about ten years ago. I can't really say it helped me understand field theory. The book that really made a breakthrough for me (YMMD) was Hatfield, Quantum Field Theory of Point Particles and Strings. This book is pretty useless as a general reference but it is very intuitive, somewhat in the style of Zefram_C's explanations, but with all the math, too.

 

[Haelfix]

Some of Dyson's original papers on the subject are also informative, and quite readable. It explains the link between canonical quantization and the path integral. So if you understand the former things are well off.

I still love A Zee's book, Quantum field theory in a Nutshell. Its a very quick read, is wonderfully intuitive and quite deep. You pretty much have the path integral thrown at you right from the getgo, and its only a few chapters before its almost fully justified.

 

[Feynman]

So gentelmen,
How we can interprate for exemple the excat solution of Shrodinger equation for harmonic oscilator by Feynmanpath integral?
which is very complex

 

[Feynman]

OHHHHH
If i can't buy the book, what i do?

 

[Feynman]

what is the probabilisitic point view about path integral?

 

[Feynman]

Please what is the probabilisitic point view about path integral?

 

[Feynman]

What is the relation between Manifolds and the path integral?
Thanks

 

[Feynman]

What is the differential geometry role on path integral?

 

[jtolliver]

Please what is the probabilisitic point view about path integral?

The probability of traveling from one point to the other is the sum over all paths between them of the probability of traveling along that path; The path integral is basically just that sum over paths.

 

[Feynman]

So can we consider that the path integral is an integral over manifolds?

 

[Feynman]

So can we consider that the path integral is an integral over manifolds?

 

[Feynman]

So can we consider that the path integral is an integral over manifolds?

 

[Feynman]

?

 

[Mike2]

So can we consider that the path integral is an integral over manifolds?

Paths are manifold.

 

[Feynman]

Who and why Paths are manifold Mike?
I'm talking about path integrals

 

[selfAdjoint]

Mike means that a path (a one-dimensional continuum) is a manifold. A one-dimensional manifold. But I am sure that wasn't what you meant. But I can't figure out what you did mean.

 

[Mike2]

Mike means that a path (a one-dimensional continuum) is a manifold. A one-dimensional manifold. But I am sure that wasn't what you meant. But I can't figure out what you did mean.

I've taken to re-reading about path integrals to see if I can get a better intuition of what's going on. Hatfield's presentation seems to be the best I've seen so far - not so many things pulled out of the hat.

In (my) words, it is the integral over all possible paths of the exponential of "i" time the action. The "e" to the "i" of something is always less than or equal to one. This is the weight given to each path in the sum? So I wonder, what values can the Action take? Can it be anything from zero to infinity? Can it be negative? Thanks.

 

[selfAdjoint]

Mike, e to the power i times something is always a complex number of modulus (i.e. magnitude) 1. THe "something", a function of time, shows the angle the number makes with the real axis. As Feynman says in QED, think of a "little arrow" of length 1 that can point anywhere in a 360^o circle, like a dial or a compass needle. As the particle travels, the vector representing the exponential rotates around at a steady rate (because the exponent of e was a linear function of time). So at every point on the path it is pointing somewhere or other, and all the paths are like that they all have little arrow pointing at some angle in the plane. It's better to think of each path having a dial somewhere outside of the spacetime picture where the pointer can go around. This is all really metaphor for complex numbers.

So then you add up (integrate) all the complex values along each path and then integrate the sums across all the paths, and what happens is that all the different pointing arrows wash each other out and only the classical path comes out of the integration.

 

[Mike2]

Mike, e to the power i times something is always a complex number of modulus (i.e. magnitude) 1.

So each "path" is weighted by the same magnitude but different phase?

So then you add up (integrate) all the complex values along each path and then integrate the sums across all the paths, and what happens is that all the different pointing arrows wash each other out and only the classical path comes out of the integration.

I'm sure there is a little more to then that. The path integral does not result in a classical path; for then there would be no need for path integral in the first place. I think it means that the classical path simply contributes most to the path integral than for the far fetched paths, right?

 

[selfAdjoint]

First question, yes if it's just the $$e^{i\psi t}$$, but you can have multipliers of the whole exponential that change the modulus. The key is Euler's relation: $$me^{i\theta} = mcos\theta + imsin\theta$$.

Second question, no, there is AFAIK no reason prior to Feynmann's method that quantum amplitudes should give the classical (stationary action) path.

 

[Feynman]

So gentelman ,
we are taking about the Path which mean (maybe) manifolds, and not complex .
My question is why the path can be consider that is a manifold and can be consider the path integral is an integral over a manifold?
Thanks