Vacuum diagrams vs. tree diagrams vs. loop diagrams

[Higgsy]

Could someone please tell me the difference between tree diagrams and loop diagrams? If I'm thinking correctly tree diagrams are before contracting? Also how do vacuum diagrams fit into the picture?

Thanks!

 

[Orodruin]

Could someone please tell me the difference between tree diagrams and loop diagrams?

A tree diagram is a diagram which does not contain loops. A diagram contains (at least) a loop if it is possible to go along edges and return to the same point without backtracking along the same edges. If you are topologically inclined, a diagram ##T## is a tree diagram if it has a trivial first homotopy group ##\pi_1(T)##. An ##n## loop diagram ##D_n## has the first homotopy group ##\pi_1(D_n) = \mathbb Z_2^n##.

 

[Higgsy]

And vacuum diagrams are just diagrams without vertices?

 

[Orodruin]

And vacuum diagrams are just diagrams without vertices?

No, vacuum diagrams are diagrams without external legs.

 

[Higgsy]

Oh right of course. Sorry it's getting late... thanks!

 

[David Neves]

Isn't the only way it can detected by by the external legs? How could it's presence could be in any detected without external legs? For example, it's the Casimir Effect a closed loop effect, with external legs, in the same way the Lamb Shift is a closed loop effect with external legs?