What is a generating function (GF) in physics?

[Living_Dog]

I am trying to understand CM wrt QFT and found out that I need to understand the HJE. This brought me to reading about all related subjects. The history lesson alone has been awesome. However, now I am reading about the HJE and found the Wikipedia pages lacking as to exactly what is the nature/idea behind/role of GF's in physics.

[1] GF's in CM
Wikipedia.com says: "Generating functions which arise in Hamiltonian mechanics are quite different from generating functions in mathematics. In the case of physics, generating functions act as a bridge between two sets of canonical variables when performing canonical transformation."

So F(q,P,t) => Q and p can be determined from this F? So F "generates" Q and p??

[2] GF's in E&M:
I recall that there is an equation of motion in E&M which has a delta function as a "generating function" solution.

NOTE: I don't need the physics - I need the _idea_ of what a GF is ... and now that I think about it - are they related?

Thanks in advance.

-LD
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[Dyson]

To get the solution of a partial differential equation with a inhomogeneous term ,we introduce the delta function on the right side of the equation.The corresponding solution is called Green function.I don,t think GF's in E&M has some relations with GF's in CM.The GF's in CM only helps us link the old canonical variables with the new canonical variables during the transformation.

 

[Living_Dog]

To get the solution of a partial differential equation with a inhomogeneous term ,we introduce the delta function on the right side of the equation.The corresponding solution is called Green function.I don,t think GF's in E&M has some relations with GF's in CM.

D'OH! You are right sir! - my bad ... and apologies.

The GF's in CM only helps us link the old canonical variables with the new canonical variables during the transformation.

So that's all the four types of generating functions do - is relate the old canonical coordinates to the new ones!

Thanks for the awesome help! I can now move on in my studies.

-LD
__________________
my faith: http://www.angelfire.com/ny5/jbc33/

 

[Dyson]

It's my pleasure!