All Questions
12
questions
1
vote
0
answers
70
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
1
answer
247
views
Physical interpretation of thermal 2-point function in QFT
Let $\phi$ be a scalar field, $\rvert \psi_i \rangle$ a set of multiparticle states living in the Fock space of the theory indexed over the naturals, with definite 4-momentum. Let $$\rho_i = \frac{e^{-...
- 152
1
vote
0
answers
98
views
The Quantum Statistical Average of the Energy-Momentum Tensor
Here: https://arxiv.org/abs/1009.3521 and here: https://arxiv.org/abs/1410.6332 as well as elsewhere, the quantum statistical average of the energy-momentum tensor is taken to be
\begin{equation} \...
- 321
1
vote
0
answers
103
views
How is the path-integral over a spatially finite region calculated?
The partition function for a system in the path-integral formalism is given by
\begin{equation}
\mathcal{Z}=\int\mathcal{D}\psi\mathcal{D}\psi^{\dagger}{e^{\int_0^{\beta}d\tau\int_Vd^3x\mathcal{...
- 321
2
votes
0
answers
93
views
Relation of Wick theorems
In the context of quantum stat mech it is common to use Wick's theorem to refer to the factorisation
$$
\langle f_1 f_2 f_3 \cdots f_N\rangle = \sum_{\text{pairings}\, \pi} (\pm 1)^{|\pi|} \langle f_{\...
- 1,094
5
votes
2
answers
533
views
What does the Temperature of a QFT physically mean?
In elementary statistical mechanics, one can think of temperature as arising from the average kinetic energy of particles in the ensemble. Is there a similar way to think about the temperature of a ...
- 1,055
3
votes
1
answer
597
views
Finite temperature quantum field theory
In a QFT at finite temperature we consider the Euclidean time to be periodic, i.e. we consider a theory on the manifold $\mathbb{R}^{d - 1} \times S^1$, where the spatial coordinates are in $\mathbb{R}...
- 401
1
vote
0
answers
320
views
Fermion boundary condition for a thermal compact circle
Is this true that for fermion statistical systems
in the thermal phase, with Euclidean time,
$$
\beta=1/T=t_E
$$
the Euclidean time will be chosen to be anti-periodic for fermion boundary ...
- 4,336
0
votes
1
answer
214
views
Role of thermal fluctuations in restoring the symmetry in finite systems
A symmetry is spontaneously broken in a system with infinite number of degrees of freedom (DOF), when the system finds itself in the ground state that breaks the symmetry of the Hamiltonian. For ...
- 26.8k
1
vote
0
answers
302
views
What is the meaning of thermal spectral function and thermal decay width in thermal field theory?
In Kallen-Lehmann spectral representation of 2-point correlation function
\begin{equation}
\langle 0|T\phi(x)\phi(0)|0\rangle=\int_0^\infty \frac{dM^2}{2\pi}\rho(M^2)D_F(x-y;M^2),\quad (a)
\end{...
- 883
19
votes
2
answers
2k
views
Proof of Loss of Lorentz Invariance in Finite Temperature Quantum Field Theory
In the standard quantum field theory we always take the vacuum to be a invariant under Lorentz transformation. For simple cases, at least for free fields, is very simple to actually prove this.
Now ...
- 2,589
21
votes
1
answer
2k
views
Duality between Euclidean time and finite temperature, QFT and quantum gravity, and AdS/CFT
The thoughts below have occurred to me, several years ago (since 200x), again and again, since I learn quantum field theory(QFT) and statistical mechanics, and later AdS/CFT. It is about the duality ...
- 7,848