All Questions
Tagged with quantum-field-theory statistical-mechanics
304
questions
2
votes
1
answer
194
views
Wick's Theorem and Functional Derivative
In the Quantum Field Theory An Integrated Approach, Fradkin, the author derived the partition functional for a free scalar field (after analytic continuation to imaginary time ) as
$$Z_{E}[J]=Z_{E}[0] ...
- 381
2
votes
1
answer
208
views
The effect of the non-existense of longitudinal polarisation mode of the photon on equipartition theorem
Massless vector bosons like photons only have 2 independent polarisation degrees, unlike massive vector bosons. For a spin 1 boson with mass $\mu$ and with $k^λ = (ω, 0, 0, k)$ the longitudinal mode ...
- 1,580
0
votes
0
answers
37
views
How to Understand the First Term in the Calabrese-Lefevre Distribution?
I am currently reading the following paper and I am trying to understand the first term in equation (6) (reproduced below):
$$
P(\lambda) = \delta(\lambda_\text{max} - \lambda) + \frac{b \Theta(\...
user261609
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
2
votes
1
answer
61
views
How to Prove A Claim made to Construct the Calabrese-Lefevre Distribution?
My question is a mathematical one based on this physics paper. Suppose that $\lambda_i $ is an eigenvalue of a reduced density matrix. Up to a normalization factor, the distribution of eigenvalues is ...
user261609
2
votes
0
answers
93
views
Relation of Wick theorems
In the context of quantum stat mech it is common to use Wick's theorem to refer to the factorisation
$$
\langle f_1 f_2 f_3 \cdots f_N\rangle = \sum_{\text{pairings}\, \pi} (\pm 1)^{|\pi|} \langle f_{\...
- 1,094
7
votes
0
answers
125
views
Slowest possible correlation decay in classical lattice models
Consider lattice models in classical statistical mechanics, like the Ising model, specified by the Gibbs ensemble of a (real-valued) local lattice Hamiltonian. What's the slowest that correlation ...
- 935
8
votes
3
answers
448
views
Relation between Spontaneous Symmetry Breaking and Renormalization Group
I have two different pictures in my head of how a phase transition occurs, but I am not sure of the relation between these two pictures.
SSB: Our theory has a global symmetry and when the parameters ...
- 642
6
votes
1
answer
199
views
Does a $d$-dimensional stat-mech theory necessarily have a $(d-1)$-dimensional quantum theory equivalence?
A $d$-dimensional stat-mech theory on a lattice usually can be represented by a $d$-dimensional tensor network. Taking a row/slice of tensors ($M$ tensors or sites) as the transfer matrix (MPO in 2$d$ ...
- 356
4
votes
1
answer
609
views
Is there a notion of a "Majorana boson"?
In a similar manner to how we can define Majorana fermionic operators $\gamma_j$ via
$$
c_j \propto \gamma_{2j+1} + i \gamma_{2j}^\dagger,
$$
where the $c$'s are fermionic creation/annahilation ...
- 1,544
0
votes
0
answers
311
views
Free Energy vs. Partition Function in QFT
The partition function of QFT is defined as
$$Z=\int\mathcal{D}\varphi e^{iS[\varphi]}.$$
Now, it is a general fact that this formal path integral can be computed perturbatively as (sketchy)
$$Z=\sum_{...
- 854
1
vote
1
answer
96
views
What is the relation between joint measurability and common refinement (pure state decomposition) of density operators?
Here page 13, the author states "...just as two quantum observables are often not jointly measurable, two
decompositions of mixed states often have no common refinement (Actually, in
the ...
- 51
0
votes
0
answers
172
views
Connection between the imaginary part of retarded correlation function and derivative of Fermi-Dirac distribution function
A two-particle retarded correlation function is (its derivation is not related to my question here)
$$
C^R(\omega) = \sum_{kq}\bigg(f(\epsilon_k )-f(\epsilon_{k+q} )\bigg)\frac{1}{\omega+\epsilon_k-\...
- 1,335
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
5
votes
0
answers
276
views
Absence of Symmetry Breaking in 1D Ising Model--Continuum Version
I have seen arguments for why there is no symmetry breaking in the 1D Ising model--for example, using the transfer matrix method to explicitly solve the model, and another of energy-entropy arguments ...
- 642