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4
questions
4
votes
2
answers
425
views
Interpreting generating functional as sum of all diagrams
The generating functional is defined as:
$$Z[J] = \int \mathcal{D}[\phi] \exp\Big[\frac{i}{\hbar}\int d^4x [\mathcal{L} + J(x)\phi(x)]\Big].$$
I know this object is used as a tool to generate ...
- 3,350
1
vote
0
answers
431
views
Connected Diagrams [duplicate]
The generating functional for the connected part of the Green functions is defined
as
$$iW[j] = \log Z[j].$$
From this the four-point connected Green's function is then given by
$G_c(x_1,x_2,x_3,...
- 445
13
votes
2
answers
6k
views
Intuition behind Linked Cluster Theorem: connected vs. non-connected diagrams
Within statistical physics and quantum field theory, the linked cluster theorem is widely used to simplify things in the calculation of the partition function among other things.
My question has the ...
- 7,931
6
votes
2
answers
2k
views
How to prove useful property of logarithm of generating functional in QFT?
How to prove that $\ln(Z(J))$ generates only connected Feynman diagrams? I can't find the proof of this statement, and have only met its demonstrations for case of 2- and 4-point.
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