All Questions
10 questions
3votes
1answer
130views
Green function power-law behavior in real and momentum space
Given a Green's function with pawer-law behavior in $k$-space $g(k)\sim\frac{1}{k^a}$ (at least for small $k$), what is the asymptotic form for $g(x)$ in the real space? In the paragraph above Eq. (56)...
- 3,942
1vote
0answers
140views
Combinatorics for Feynman Diagrams [closed]
When one wants to calculate the two-point-function for an electronic system with Coulomb-interactions in quantum many body systems with the path-integral-formalism $$ \mathscr{G}_{ \alpha , \alpha^{ \...
- 343
2votes
1answer
117views
When is static limit ($\omega=0$ and then $q=0$) of correlation function physical and used?
For a general correlation/response function $F(q,\omega)$, it can be both frequency and momentum dependent. And there are the so-called transport limit $$q\rightarrow0 \text{ and then }\omega\...
- 3,942
5votes
2answers
409views
Why are time-ordered Greens functions equal to retarded Greens functions at zero temperature?
When I calculate a photon polarization diagram: I get the same answer: If I calculate it in equilibrium (retarded Greens functions) with finite chemical potential, in the limit of zero temperature, ...
- 1,697
0votes
2answers
186views
Why is the correlation matrix $C_{ij}=\langle c^{\dagger}_i c_j \rangle$ Hermitian? [closed]
Suppose we are working with free fermions so that an eigenstate $|\psi\rangle$ is a tower of single particle states, i.e.: $$ d_k \propto \sum_n e^{ikn}c_n \quad \text{so that} \quad |\psi^{N_p}\...
- 1,501
4votes
0answers
141views
How to calculate the "vortex" correlation function in 2D free system?
I want to calculate the following correlation function in 2D square lattice: $$G(i, j, \tau) \equiv\left\langle e^{-\frac{i}{2}\left[\hat{\Phi}_{i}(\tau)-\hat{\Phi}_{j}(0)\right]}\right\rangle_{0}$$ $\...
- 1,682
1vote
4answers
482views
Monopole operator: correlation functions
Let's consider free Maxwell theory: $$ S_{Maxwell} = \int d^dx \; -\frac{1}{4e^2}F_{\mu\nu}F^{\mu\nu} $$ In such theory one can define monopole operator using path integral via correlation functions ...
- 5,757
5votes
0answers
239views
Double the number of degrees of freedom for the Schwinger-Keldysh (in-in) formalism
I am studying the Schwinger-Keldysh (in-in) formalism. Basically, we double the number of degrees of freedom for the upper and lower branches. Let´s consider the case where we have a certain field, ...
- 51
4votes
0answers
327views
A confusing point in linear response theory on the ground state
Information about a quantum system could be drawn from its response to a small perturbation. This is formulated in what is known as linear response theory. In second quantization, consider a ...
7votes
2answers
3kviews
How to determine correlation length when the correlation function decays as a power law?
I am studying a system for which I observe a power-law decay in the correlation function: $\left\langle s\!\left(0\right)\cdot s\!\left(r\right) \right\rangle \propto r^{-\alpha}$ I am interested in ...
- 819
