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Living_Dog
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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
__________________
[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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