All Questions
43
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
1
vote
0
answers
76
views
physical interpratation of partition function in Quantym field theory
Partition function in Statistical mechanics is given by
$$ Z = \sum_ne^{-\beta E_n} $$
For QFT, it is defined in terms of a path integral:
$$ Z = \int D\phi e^{-S[\phi]} $$
How can we see the relation ...
- 411
0
votes
1
answer
62
views
Chern-Simons theory: Connection between Thermal and Quantum Partition Function
I have been reading the Quantum Hall Effect from Prof. David Tong's notes. In the section on Chern-Simons theory, he describes the connection between the Thermal Partition Function and the Quantum ...
- 1
2
votes
0
answers
97
views
What is the action of fermionic Hamiltonian $\mu_1 n_1 + \mu_2 n_2 + U n_1 n_2$
Problem
Consider a Hamiltonian
\begin{equation}
H(c^\dagger, c) = \mu_1 c_1^\dagger c_1 + \mu_2 c_2^\dagger c_2 + U c_1^\dagger c_1 c_2^\dagger c_2\,,
\end{equation}
where $c_i$ are fermionic ...
- 191
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
56
views
Landau Ginzburg path integral (PI) for the Ising model at gaussian order
I am stick with a problem in computing explicitely the gaussian PI in the Landau-Ginzburg theory for the Ising model.
If we do a procedure of coarse graining, we can define $m(x)$ as a continuous ...
3
votes
1
answer
167
views
Generating functional for fields with non-zero expectation value
When doing QFT or statistical field theory of, say $N$ scalar fields $\varphi_i$, we consider the the generating functional
$$
W[J] = - \ln Z[J], \quad Z[J] = \int \mathcal D \varphi \, e^{-S[\varphi] ...
- 577
4
votes
0
answers
60
views
Thermodynamic free energy of interacting system
This question concerns an interacting system's thermodynamic free energy $\Omega$. Generally speaking, The action $S$ for an interacting system has the following form:
\begin{equation}
S(\phi,\psi) = ...
- 2,038
4
votes
0
answers
128
views
Is the path integral emergent?
I have recently read a couple of papers on lattice QCD and found that there is a well-established connection between Boltzmann distribution and the path integral in QFT (disclaimer: I am not a huge ...
4
votes
1
answer
257
views
Connection between a saddle point approximation and plain perturbation theory
I am currently studying functional integration in the context of classical and quantum equilibrium thermodynamics. However one thing puzzles me:
In the book "Phase Transitions and Renormalization ...
- 155
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
3
votes
0
answers
73
views
Can the QFT path integral be re-expressed using a real, positive-definite function of the action? [duplicate]
This question is based on my rather shaky grasp of QFT, so if I'm missing a key concept then just let me know!
If you're deriving the Schrodinger equation from the path integral as Feynman did, then ...
- 2,475
2
votes
1
answer
160
views
How to find the QM propagator for more general quadratic theories? (and why didn't my attempts work?)
The Problem
I'm working on a problem using the Path Integral approach to quantum mechanics. Actually, more accurately I'm interested in the Wick rotated version of the problem, so I suppose ...
- 21
1
vote
1
answer
272
views
Average value of creation and annihilation operators - are these two expressions the same?
Suppose we want to study many-fermions quantum mechanics on a lattice, so we start with a finite-dimensional Hilbert space $\mathcal{H}$ and go to its Fock space $\mathcal{F}_{\text{fer}}(\mathcal{H})$...
- 1,131
1
vote
1
answer
83
views
Clarification regarding the terminology of Microstates
I would like to understand how microstates are defined or used in physics. Are microstates suppose to only mean eigenvalues of a given observable (or a generator of symmetry)? The reason for my ...
- 1,200