All Questions
8
questions
1
vote
0
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72
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Calculating $\langle\hat{\phi_i}\rangle_t$ (Blundell's Quantum field theory) (EDITED) [closed]
I am reading Blundell's Quantum field theory for the Gifted Amateur and stuck at some calculation. In his book p.197, 21.2 Sources in statistical physics, he defined the partition function with the ...
- 323
-2
votes
1
answer
389
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Correlation Function and Generating Functional in QED
Peskin and Schroeder (1995, p.82 and p.292) define the two-point correlation function of a $\phi^4$ theory as
$$\langle \Omega|T\{\phi(x)\phi(y)\}|\Omega\rangle\tag{4.10}$$
and the generating ...
- 373
12
votes
2
answers
505
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How to calculate a TQFT Gaussian path integral from Seiberg's "fun with free field theory"?
In his talk "Fun with Free Field Theory", Seiberg discusses a topological quantum field theory in $d+1$ dimensions with the action
$$ S = \frac{n}{2\pi} \int \phi\, \mathrm{d} a \tag{1}$$
...
- 2,084
2
votes
2
answers
247
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Calculating generating functional with stationary phase approximation
Let's say that I have a generating functional $Z[J]$ defined as:
\begin{equation*}
Z[J]=\int \mathcal{D}\phi\,e^{iS[\phi]+i\int d^4x\,J\phi}.\tag{1}
\end{equation*}
I want to use the stationary phase ...
- 2,613
6
votes
2
answers
1k
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Correlation Function of One-Dimensional XY Model
From the Harvard lecture notes XY model: particle-vortex duality by Subir Sachdev, the path-integral of 1D XY-model is given by
$$\mathcal{Z}=\int\mathcal{D}\theta\exp{\left\{-\frac{K}{2}\int \!dx~(\...
- 2,923
9
votes
1
answer
874
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Is there any physical meaning for such a correlation function?
Consider a thermal scalar field theory, we have the partition functional
$$Z={\rm tr}(e^{-\beta H}).$$
We can build this theory as an Euclidean quantum field theory
$$Z=\int\mathcal{D}\Phi\,e^{-S_E[\...
- 3,691
5
votes
2
answers
830
views
Can we define partition function for a classical field theory?
I heard that $d$ dimensional relativistic quantum field theory can be viewed as a $d+1$-dimensional statistical mechanics. Can a relativistic/non-relativistic classical field theory be also looked ...
- 26.8k
1
vote
0
answers
138
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How to use the generating functional for connected functions to compute connected diagrams? [duplicate]
We have
$$W[J]\equiv\hbar i\log(Z[J])$$
How do we use it to compute the connected diagrams to some order in perturbative field theory?
I get that we need to take functional derivatives of ...
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