All Questions
Tagged with quantum-field-theory statistical-mechanics
304
questions
3
votes
3
answers
594
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
43
views
Precise relation between theromdynamic beta and coupling constant in Euclidean QFT
In statistical mechanics, the thermodynamic is inverse of the temperature: $\beta \propto T^{-1}$.
In Euclidean QFT, I have often run into the expression like $\beta \propto g^{-2}$ where $g$ is the ...
- 1,665
1
vote
0
answers
75
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
1
vote
0
answers
68
views
Intuition for imaginary time Greens function
I understand that $$G^M(0,0^+) = \operatorname{tr}\{\rho O_2 O_1\}$$ (I am not putting hats on the operators here because they don't render in the correct position) is simply the expectation value of ...
- 21
0
votes
0
answers
74
views
Operator Product Expansion (OPE) coefficients of free massless theory
Consider the action of the free massless bosonic theory in $2+1D$
$$
S = \int d^3x \partial_{\mu}\phi(x) \partial^{\mu} \phi(x).
$$
The single-particle spectrum (on the surface of a sphere) is given ...
- 11
1
vote
0
answers
36
views
Does the changes of flow regimes of the renormalization group flow diagram imply always that a symmetry has been broken?
Usually we can use RG flow diagrams to understand that a phase transition has happened. Because they are intimately related to a broken symmetry, does that imply that it always implies that a symmetry ...
- 11
3
votes
1
answer
122
views
Why can't bosonic systems have fermionic excitations?
When reading Abrikosov's book AGD, there is a statement that 'It is obvious only that a Bose system can not have excitations with half-integral spins' (page 5).
I don't understand why this is the case....
- 51
2
votes
0
answers
75
views
Different ways to understand fermions [closed]
I first learned about fermions in my atomic physics class, where the teacher said that electrons obey the Pauli exclusion principle. Later, in my quantum mechanics class, I learned about identical ...
- 368
0
votes
0
answers
38
views
Calculation of conformal dimension for Ising model in two dimensional space
Recently I was reading Ph. Di Francesco's book, "Conformal Field Theory", and in section 7.4.2 where it discussed about Ising model, conformal dimensions $(h,\bar{h})$ are deduced from ...
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
0
votes
0
answers
28
views
How to relate the two expressions of thermal spectrum?
I am reading a proof of the fact that if there exists a monochromatic plane electromagnetic wave for an observer in frame $S$, an observer in a frame $S'$, which is uniformly accelerated with respect ...
- 108
3
votes
1
answer
82
views
Is RG fixed point always related to a second-order phase transition?
In practice, usually one of the parameters is tuned (for example temperature in 3D Ising model, which is a relevant parameter) so that it coincides with the value of RG fixed point, then RG flow make ...
- 619
2
votes
0
answers
96
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
0
answers
172
views
Is there any renormalization group with infinite number of generators that does not satisify a renormalization group equation?
A generating set of a semigroup(monoid) is a subset of the semigroup set such that every element of the semigroup can be expressed as a combination (under the semigroup operation) of finitely many ...
2
votes
1
answer
118
views
Thermal ground state?
Consider a system of $N$ fermions in a periodic box $\Lambda \subset \mathbb{R}^{d}$, described by the Hamiltonian
$$H_{N} = \sum_{k=1}^{N}(-\Delta_{x_{k}}-\mu) + \lambda \sum_{i< j}V(x_{i}-x_{j}) \...
- 1,123