All Questions
11
questions
3
votes
3
answers
608
views
Path integral at large time
From the path integral of a QFT:
$$Z=\int D\phi e^{-S[\phi]}$$
What is a nice argument to say that when we study the theory at large time $T$, this behaves as:
$$ Z \to e^{-TE_0} $$
where $E_0$ is the ...
- 411
2
votes
1
answer
176
views
Examples of Path integral $\neq$ Partition function?
Are there any systems we know of whose partition function is not simply Wick rotation of the path integral? Does anyone know of any examples?
- 1,200
1
vote
0
answers
61
views
Is the Euclidean generating functional $Z_{E}[J]$ identified with original Minkowskian generating functional $Z[J]$?
In quantum field theory, it is common to perform wick rotation $t\rightarrow -i\tau$ and get Euclidean generating functional $Z_{E}[J]$. When I first studied QFT, I just saw this a magic trick to ...
- 81
6
votes
1
answer
199
views
Does a $d$-dimensional stat-mech theory necessarily have a $(d-1)$-dimensional quantum theory equivalence?
A $d$-dimensional stat-mech theory on a lattice usually can be represented by a $d$-dimensional tensor network. Taking a row/slice of tensors ($M$ tensors or sites) as the transfer matrix (MPO in 2$d$ ...
- 356
1
vote
0
answers
248
views
Quantum to classical mapping
I'm having troubles understanding precisely how the mapping from a quantum system to a classical one works.
Let's say that I have a quantum system in $d$ dimensions with Hamiltonian $H$ at temperature ...
- 741
4
votes
1
answer
424
views
In QFT, why are the vacuum partition function and the zero-temperature imaginary-time partition function the same?
When doing thermal field theory, one can start with the definition of the (thermal) partition function $Z = Tr[e^{-\beta H}]$, and inserting a number of completness-relations, we can arrive at (I am ...
- 577
1
vote
0
answers
256
views
What is the entropy and/or equation of state of a partition function such as $Z=\int D\phi \exp (i S[\phi]/\hbar)$?
At this link https://en.wikipedia.org/wiki/Partition_function_(mathematics), it is claimed that the following partition function:
$$
Z=\int D\phi \exp (-\beta H[\phi]) \tag{1}
$$
is a consequence of ...
- 1,548
4
votes
0
answers
311
views
Extra $i$ in grand canonical partition function: why the Wick rotation?
Going through my notes I stumbled upon something I can't wrap my head around.
I'd like to write the grand canonical partition function for a system of identical charged particles (charge $e$) ...
- 616
9
votes
1
answer
874
views
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
63
votes
4
answers
6k
views
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
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