Author Topic: Path Integral Simplified  (Read 911 times)

Offline josephpalazzo (OP)

Path Integral Simplified
« on: May 12, 2014, 08:23:49 AM »
You’ve probably heard many crazy ideas, and most of the time, they are just that, crazy. But once in a while one of those crazy ideas turns out to be correct. Feynman’s idea of the path integral was one of those crazy ideas. In this blog, you will see how Feynman put his "crazy" idea into a mathematical formulation with results that were equivalent to QFT.

Path Integral Simplified

Any comments would be appreciated.

Re: Path Integral Simplified
« Reply #1 on: May 13, 2014, 05:29:59 AM »
I got as far as time slicing before my brain gave out. 
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Offline josephpalazzo (OP)

Re: Path Integral Simplified
« Reply #2 on: May 13, 2014, 06:38:55 AM »
There's an anecdote as told by Zee in Quantum Field Theory in a Nutshell :

In a double-slit experiment, a student asked: "what if you bore a third hole in the screen?" The professor replied,"Clearly, the amplitude for the particle to be detected at O is now given by the sum of three amplitudes." The professor was just about to continue  when the student interjected again, "What if I drill a fourth and a fifth hole in the screen?" Now the professor is losing patience, "All right, wise guy, it is obvious that we just sum over all holes. "  But the student said, "What if I drill an infinite number of holes so that the screen is no longer there?" The professor sighed:" Let's move on, there's a lot of material to cover in this course". That student was Richard Feynman.


Re: Path Integral Simplified
« Reply #3 on: May 13, 2014, 11:40:11 AM »
You’ve probably heard many crazy ideas, and most of the time, they are just that, crazy. But once in a while one of those crazy ideas turns out to be correct. Feynman’s idea of the path integral was one of those crazy ideas. In this blog, you will see how Feynman put his "crazy" idea into a mathematical formulation with results that were equivalent to QFT.

Path Integral Simplified

Any comments would be appreciated.

If you can explain this so Casparov realizes it's about particles you are a genius. Solitary
There is nothing more frightful than ignorance in action.

Re: Path Integral Simplified
« Reply #4 on: May 13, 2014, 11:44:40 AM »
There's an anecdote as told by Zee in Quantum Field Theory in a Nutshell :

In a double-slit experiment, a student asked: "what if you bore a third hole in the screen?" The professor replied,"Clearly, the amplitude for the particle to be detected at O is now given by the sum of three amplitudes." The professor was just about to continue  when the student interjected again, "What if I drill a fourth and a fifth hole in the screen?" Now the professor is losing patience, "All right, wise guy, it is obvious that we just sum over all holes. "  But the student said, "What if I drill an infinite number of holes so that the screen is no longer there?" The professor sighed:" Let's move on, there's a lot of material to cover in this course". That student was Richard Feynman.


That really is a good question, and I'd like to know the answer---an Aleph of particles? Solitary
There is nothing more frightful than ignorance in action.

Offline josephpalazzo (OP)

Re: Path Integral Simplified
« Reply #5 on: May 13, 2014, 02:21:36 PM »
That really is a good question, and I'd like to know the answer---an Aleph of particles? Solitary

The answer is in the OP: the Path Integral.

Offline josephpalazzo (OP)

Re: Path Integral Simplified
« Reply #6 on: May 14, 2014, 08:13:44 AM »
I got as far as time slicing before my brain gave out. 
It's not much different than integrals, just the time is parceled and use the sum instead of an ordinary integral.

Re: Path Integral Simplified
« Reply #7 on: May 14, 2014, 07:15:28 PM »
You’ve probably heard many crazy ideas, and most of the time, they are just that, crazy. But once in a while one of those crazy ideas turns out to be correct. Feynman’s idea of the path integral was one of those crazy ideas. In this blog, you will see how Feynman put his "crazy" idea into a mathematical formulation with results that were equivalent to QFT.

Path Integral Simplified

Any comments would be appreciated.

I believe the correct answer is 42.
Carl Sagan
"It is far better to grasp the universe as it really is than to persist in delusion, however satisfying and reassuring."