All Questions
Tagged with quantum-field-theory partition-function
21
questions
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.
- 6,564
8
votes
4
answers
5k
views
Proof of Connected Diagrams
If $Z[J]$ is the generating functional for the path-integral, could any prove (or more reasonably, refer me to a proof) that $$W[J]\equiv\frac{\hbar}{i}\log\left(Z[J]\right)$$ "generates" only ...
- 2,024
63
votes
4
answers
6k
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How exact is the analogy between statistical mechanics and quantum field theory?
Famously, the path integral of quantum field theory is related to the partition function of statistical mechanics via a Wick rotation and there is therefore a formal analogy between the two. I have a ...
- 3,492
13
votes
2
answers
3k
views
Physical meaning of partition function in QFT
When we have the generating functional $Z$ for a scalar field
\begin{equation}
Z(J,J^{\dagger}) = \int{D\phi^{\dagger}D\phi \; \exp\left[{\int L+\phi^{\dagger}J(x)+J^{\dagger}(x)}\phi\right]},
\end{...
- 1,336
8
votes
1
answer
975
views
Srednicki's Path Integrals: Ground-State to Ground-State Transition Amplitude in the Presence of a Perturbation
Srednicki's Quantum Field Theory mentions the following at the end of the unit on path integrals in non-relativistic quantum mechanics:
Assume that the total Hamiltonian is of the form,
$$ H = H_0 + ...
- 705
4
votes
1
answer
503
views
How are second-class constraints handled in the path integral formulation?
A first-class constraint is typically associated with a gauge redundancy. In order to account for this in the path integral, we simply integrate over only gauge-inequivalent configurations. This is ...
- 103k
2
votes
1
answer
264
views
Supersymmetric Localization (Mirror Symmetry)
I'm reading Chapter 9 of Mirror Symmetry book. As you can see in eq. (9.30) his model for SUSY is
$$\begin{align}
\delta_\epsilon X &=\epsilon^1\psi_1 + \epsilon^2\psi_2\\
\delta\psi_1 &= \...
- 1,536
13
votes
3
answers
4k
views
The Chern-Simons/WZW correspondence
Can someone tell me a reference which proves this? - as to how does the bulk partition function of Chern-Simons' theory get completely determined by the WZW theory (its conformal blocks) on its ...
- 4,619
11
votes
3
answers
5k
views
Relation between statistical mechanics and quantum field theory
I was talking with a friend of mine, he is a student of theoretical particle physics, and he told me that lots of his topics have their foundations in statistical mechanics. However I thought that the ...
- 630
5
votes
3
answers
2k
views
Completing the square for Grassmann variables
When working with path integrals of both bosonic and fermionic field variables, I'm a bit unsure of how to do the usual complete the square trick when an interaction between the two is concerned. Say ...
- 538
5
votes
2
answers
693
views
Vacuum Character in Compactified Boson Partition Function
For a generic $c \ge 1$ 2D CFT, I (wrongly?) expect to be able to write its torus partition function as
$$Z(\tau, \bar\tau) = \chi_0(\tau) \bar \chi_0(\bar \tau) + \sum_{(h,\bar h) \ne (0,0)}n_{h,\bar ...
5
votes
1
answer
486
views
The Partition Function of $0$-Dimensional $\phi^{4}$ Theory
My question is related with this question. Several years ago, I posted an answer to the question, and the author of the reference removed the link permanently, now I have no clue what's going on.
In ...
- 2,923
5
votes
1
answer
609
views
When does QFT perturbation theory stop being valid?
When introduced to the concept of perturbation theory in Quantum Mechanics we split the hamiltonian $H= H_0 + \delta H$ where $\delta H$ is small in some manner, ie if say $\epsilon$ is the relevant ...
- 766
4
votes
0
answers
100
views
Functional determinant: linking Series, Heat-Kernel and Zeta function
I would like to express a functional determinant as a series of diagrams, using the zeta function renormalization applied to the heat-kernel method, but I don't know if it's possible. Let me explain:
...
- 2,613