# What is a generating function (GF) in physics?

1. Jan 3, 2010

### 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???

-LD
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Last edited by a moderator: Aug 3, 2010
2. Jan 4, 2010

### 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.

3. Jan 4, 2010

### Living_Dog

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

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/

4. Jan 4, 2010

### Dyson

It's my pleasure!