Questions tagged [self-energy]
Quantum-mechanical object that captures some of the characteristics of particles associated to interactions with themselves and with other particles, such as the change in its mass as a function of its energy. Particularly useful in quantum field theory, either for relativistic particle physics or condensed matter physics. Although it also makes sense as a classical concept, it mostly has fallen into disuse nowadays.
87
questions
1
vote
0answers
51 views
Why is scalar field self-interaction quartic in the Lagrangian?
From https://www.youtube.com/watch?v=CNcTOSx2eMs at 11:34
the Higgs field is called a free field because it has no sources, no kinds of charges from which it emanates ... the fact that it is self ...
4
votes
1answer
95 views
Renormalization conditions for QED self-energies
I'm having trouble understanding renormalization conditions: what I know is that they are the conditions required so that at some point called "renormalization point" (which is usually just ...
1
vote
3answers
85 views
How could self-energy Feynman diagram be compatible with fundamental laws of physics? [duplicate]
Let's consider this electron self-energy Feynman diagram:
The electron radiates a virtual photon, that is absorbed again by the electron.
There are two points that look incompatible with fundamental ...
3
votes
1answer
94 views
Is the self-energy well-defined?
We know that we can calculate the Green function $G(\tau;\lambda)= -\langle \mathcal{T}c(\tau)c^*\rangle$ of an interacting Hamiltonian $H=H_0 + \lambda V$ using connected Feynman diagrams. Of course, ...
2
votes
1answer
51 views
Proof that the self-energy is an inverse lifetime
My question concerns the self-energy of a diagonal propagator for a single-particle lattice problem. The context is Anderson Localisation, but really it's a problem of complex analysis. I would like ...
0
votes
0answers
58 views
Yang-Mills self-energy
I am trying to write the diagrams associated with the self energy of a Yang-Mills field.
I have already computed the Feynman rules for the propagators and for a vertice of: 3 gluons; 4 gluons; 2 ...
1
vote
0answers
50 views
Hubbard-Stratonovich tranformation and Saddle point equations for the SYK model
I have been trying to understand the derivation of saddle point equations of the Sachdev-Ye-Kitaev (SYK) model. Consider, for example, https://arxiv.org/abs/1506.05111. After decoupling the eight-...
0
votes
0answers
46 views
One loop diagram for given interaction term
For a given interaction term, say $\frac12g\varphi^2\psi$, how would one find the one loop diagram that contributes to its self energy of $\varphi$? I think it would just be one propagator going into ...
2
votes
1answer
92 views
Wick rotation from Minkowski Dirac theory to Euclidean Dirac theory: $\gamma^{0} = -i\gamma^{4}$
I am reading Path Integrals and Quantum Anomalies by Kazuo Fujikawa and Hiroshi Suzuki. In chapter 4.2 they calculate the self-energy of photon for QED and say that the actual calculation is performed ...
3
votes
0answers
106 views
BCS and Feynman Diagrams
I am currently studying the strong coupling theory (by Eliashberg) of superconductivity, which is derived by BCS by considering self-energy diagrams and the following interaction potential
$$ V(q, i\...
1
vote
0answers
89 views
Dimensional analysis and more: Order of divergences in the $\phi^4$ theory
On page 324 of his book on qft, Peskin analyzes the superficial degree of divergence of the 1-loop self-energy correction of the $\phi^4$ scalar theory. Realizing that $D=2$, he concludes that the ...
2
votes
1answer
107 views
Gauge invariance of loop Diagrams
Say we have a gauge-fixed QED Lagrangian: $$\mathcal{L} = - \frac{1}{4}{F}_{\mu\nu}F^{\mu\nu}+ \frac{1}{2a}\left(\partial_\mu A^\mu\right)^2+\bar\psi_1(i\gamma^\mu D_\mu - m_1)\psi_1.$$
My question ...
0
votes
0answers
35 views
Classical point-charge self-energy in terms of momentum cut-off of QED
When computing the one-loop correction $\Sigma_2$ of the electron self-energy, Peskin & Schroeder on page 218 use Pauli-Villars regularization on a certain divergent momentum integral by making ...
0
votes
1answer
125 views
What are the sources of infinities in (unrenormalized) quantum field theory calculations?
The PSE questions and answers about this question I've found don't answer it to my satisfaction, so I am asking my own version, with the principal options I am aware of listed. Although one ...
3
votes
1answer
57 views
From 1PI function to cross section
The full propagator in QFT is the inverse of this two-point 1PI function defined as $$
\tilde{\Gamma}^{(2)}(p)=p^{2}-m^{2}-\Sigma(p)
$$
where $\Sigma(p)$ is the self-energy. I am have calculated the ...
0
votes
0answers
58 views
QCD quark self-energy, is the propagator momentum in the right direction?
For the quark self-energy diagram the amplitude is giving by:
The fermion propagator is given by $\frac{i}{\not p + l}$ in the lecture. It is not supposed to be $\frac{i}{\not p - l}$? It's seems ...
2
votes
1answer
81 views
Does a vanishing self-energy imply a Gaussian fixed point in a $\phi^4$ theory below the upper critical dimension?
Assuming a QFT description of a second-order phase transition. From the free theory, one obtains some critical exponents and one performs an $\epsilon$-expansion below the upper critical dimension. ...
5
votes
1answer
191 views
How can the connected Greens 2pt function be summed as a geometric series of the self-energy if the self-energy contains divergent terms?
In Ryder's book on QFT page 341 we can see
$$\begin{align}
D_{\mu\nu}'=D_{\mu\nu}-D_{\mu\alpha}\big(k^\alpha k^\beta-g^{\alpha\beta}k^2\big)\Pi(k^2)D_{\beta\nu}
\end{align}$$
and hence putting $D_{\mu\...
1
vote
1answer
88 views
How to derive $\imath q^\mu\mathcal{M}_ \mu(k;q;p)=0$?
\begin{equation}
\imath q^\mu\mathcal{M}_ \mu(k;q;p)=-\imath\tilde{e}\mathcal{M}_0(p;k-q)+\imath\tilde{e}\mathcal{M}_0(p+q;k)
\end{equation}
This is exactly the Ward-Takahashi identity for two ...
1
vote
2answers
121 views
Dimensional regularization of Electron self-energy from Ryder's book
I am Studying Electron self-energy using Ryder's textbook, In page 334 we can see
Defining $k'=k-pz$ and avoiding the term linear in $k'$(because it integrates to zero) gives
\begin{equation}
\Sigma(...
0
votes
0answers
52 views
Why we insert self-energy subgraphs in external lines to cancel infrared divergences completely (like in QED)?
Here we need to keep terms originating from the same line.
0
votes
1answer
53 views
Is it correct this formula for electrostatic energy?
In CGS: I know that:
$$
U_E = \frac12\sum_{i=1}^Nq_i\sum_{j\neq i}\frac{q_j}{|\mathbf{r}_i-\mathbf{r}_j|}.
$$
In the continuous. Is it correct this conclussion?
$$
U_E=\frac12\int \rho(\mathbf{r})\...
3
votes
0answers
185 views
Photon mass Infrared divergence regulization in the one-loop electron self-energy in QED
So basically I'm trying to calculate the one-loop mass and field strength counterterms from the electron's self-energy in QED using Pauli-Villars regularization (i.e. some heavy particle of mass $\...
2
votes
1answer
66 views
Self-energy of a $D$-dimensional statistical mechanical model
We consider a $D$ dimensional statistical mechanical model whose partition function is given by
$$\begin{aligned}
\mathcal{Z} &=\int \mathcal{D} \phi(x) \exp \left(-\mathcal{S}_{\phi}\right) \\
\...
3
votes
0answers
88 views
Scalar self-energy in $\mathcal{N}=4$ SYM in position space
In this paper (BMN Correlators and Operator Mixing in $\mathcal{N}=4$ Super Yang-Mills Theory, 2002), the authors give the following expression for the self-energy of the scalar propagator in $\...
1
vote
1answer
164 views
One-loop diagram self-energy
I need to find the diagram contributing to the self energy of $\varphi$. Say I had an interaction term in the Lagrangian 2 $\varphi$ real scalar fields, and one $\psi$ real scalar field, $\varphi^2\...
1
vote
1answer
68 views
Iterative Greens function calculation
I have a Hamiltonian which has an interactive and non-interactive parts.
$H = H_0 + H_I$
$H_I$ comes from the non-local electron-electron interaction and must be calculated self-consistently.
I ...
1
vote
0answers
45 views
Why is the self-energy for quarks in $d=2$ Large $N$ QCD only order $g^2$?
In an interesting article by 't Hooft , he is able to find the exact quark propagator, in the large $N$ limit of QCD. He finds that the full 1PI self-energy is given by:
$$\Gamma(p)=-\frac{g^2}{2\pi} \...
1
vote
0answers
62 views
Is the issue of self force on point charges solved by QED?
I know that classically self force is not a very tractable problem for point particles, although some attempts have been made in various ways over the years.
I also know that even in QED ...
1
vote
0answers
126 views
Using second order perturbation to calculate electron self-energy caused by electron-phonon interaction
Assume the electron-phonon interaction is given by
$$
H_{ep} = \sum_{k q} D(q) c_{k+q}^\dagger c_k (a_q + a_{-q}^\dagger).
$$
In the theory of superconductivity, the electron-electron effective ...
1
vote
1answer
129 views
Why do the Euler-Mascheroni constant $\gamma$ and $\ln 4\pi$ not show up in observables (renormalisation of electric charge)?
The one-loop contribution of the vacuum polarisation of the photon after using dimreg is given by
$$\Pi_2^{\mu\nu}= e^2 J(q) \left(\eta^{\mu\nu} - \frac{q^\mu q^\nu}{q^2}\right),$$
with the metric ...
0
votes
0answers
149 views
Feynman self-energy diagrams
In the Feynman picture, I don't understand how virtual photons in the self-energy diagram for a rest-frame electron can have energies that exceed $2m_e$. Aren't negative energy states of the electron ...
7
votes
2answers
224 views
Why isn't a quark-antiquark loop included in the photon self-energy corrections?
In QED, the Lagrangian has a term $\bar{\psi}A^\mu\psi$, which gives a correction to the photon propagator, where the loop is made of a pair electron-positron, with the 1st order diagram:
In the ...
3
votes
1answer
288 views
First-order Contribution to the Self-energy Operator
In Altand and Simons' book 'Condensed Matter Field Theory,' on page 225 they claim that the first-order contribution to the self-energy (effective mass) operator reads
$$\big[\Sigma_p^{(1)}\big]^{ab} =...
1
vote
0answers
56 views
Self-energy series expression in terms of unperturbed Green function for exited states
I would like to understand how to arrive at the series in equation (36) in this paper https://arxiv.org/abs/cond-mat/0506438, specifically
$$\Sigma(E) = V+VG'_0(E)V+VG'_0(E)VG'_0(E)V$$
where $G'_0(E)$ ...
0
votes
2answers
193 views
Symmetry factor of gluon self-energy
In Peskin & Schroeder, p.523, they give the diagram contributing to the gluon self-energy that arises from the 3-gluon vertex, and they claim that the $1/2$ factor is a symmetry factor:
How can ...
0
votes
1answer
226 views
Self-energy in two scalar Yukawa interaction
Considering the Lagrangian of two scalar fields in $d=4$:
$$\mathcal{L}=\frac{1}{2}(\partial\phi)^2-\frac{1}{2}m^2\phi^2+\frac{1}{2}(\partial\chi)^2-\frac{1}{2}M^2\chi^2-g\phi^2\chi$$
What would be ...
1
vote
1answer
115 views
Computation of the self-energy term of the exact propagator for $\varphi^3$ theory in Srednicki
In M. Srednicki "Quantum field theory", Section 14 -Loop corrections to the propagator-, the exact propagator $\mathbf {\tilde \Delta} (k^2)$ is stated as
$$\frac{1}{i} \mathbf {\tilde \Delta} (k^2)...
0
votes
1answer
199 views
How to know how the self-energy changes the mass?
Suppose we have a Green's function of the typical form
\begin{equation}
G(k)=\frac{1}{k^2-m^2-\Sigma(k)}
\end{equation}
where $\Sigma(k)$ is the self energy of that particle. How exactly can we ...
2
votes
1answer
519 views
How to obtain the quasiparticle equation from Dyson equation?
The problem is formulated as follows:
Dyson equation for zero temperature Green's function:
\begin{equation}
\left[
i\dfrac{\partial}{\partial t_1} - h(\vec{r}_1)
\right]
G(1,2)-\int d3 \Sigma(1,3)G(...
3
votes
1answer
3k views
Self-energy of conducting shell
While calculating self energy of a conducting shell we integrate $Vdq$,where $V=\frac{q}{4π\epsilon r}$, but when the $dq$ charge is bought close to the shell it changes the charge distribution on the ...
5
votes
1answer
360 views
Combinatorics geometric series two-point function
In this answer Proof of geometric series two-point function it is said:
Now what about the coefficients in front of each Feynman diagram? Due to the combinatorics/factorization involved it ...
3
votes
1answer
163 views
Are problems with self-energy of point charge in classical electrodynamics solved by field quantization?
Classical electrodynamics gives strange results when considering a moving charge in its self generated field (Abraham-Lorentz equation).
Some 50 years ago there were many efforts and publications ...
3
votes
1answer
332 views
2PI-effective action and functional derivatives
I'm trying to work out the 2PI-effective action for complex scalar fields.
Introducing a multi field index $(a,b,c...)$ the complex conjugation and all other degrees of freedoms are suppressed, and ...
6
votes
0answers
119 views
Self-energy that does not obey sum rule
Analytically, I calculated a self-energy $\Sigma(\omega)$, for which I verified that
1) $\text{Im}\big[\Sigma(\omega)\big] \leq 0$ for all $\omega$ and specifically $\text{Im}\big[\Sigma(0)\big] = 0$,...
0
votes
1answer
78 views
Problem with converting Integral to Gamma functions (from HQET heavy quark self-energy diagram)
In the calculation of HQET radiative correction, I came across the Equation:
$$\int_0^{\infty}d\lambda ~ \lambda^{-\epsilon}(\lambda+\omega)^{-\epsilon} = \frac{1}{2\sqrt{\pi}}\Gamma(\epsilon-\frac{1}{...
0
votes
0answers
103 views
Geometric series of two point function and self energy
This question is related to this question Proof of geometric series two-point function.
Suppose we have a graph $A$ with a symmetry factor $s_1$. According to Srednicki (chapter 9, eq. (9.13)) for a ...
2
votes
1answer
381 views
Proof of geometric series two-point function
In deriving the expression for the exact propagator
$$G_c^{(2)}(x_1,x_2)=[p^2-m^2+\Pi(p)]^{-1}$$
for $\phi^4$ theory all books that i know use the following argument:
$$G_c^{(2)}(x_1,x_2)=G_0^{(2)}...
1
vote
1answer
232 views
Proof of 1-particle irreducible (1PI) diagrams
If we split the effective action into
$$Γ[Φ] =\frac{1}2ΦiG_0^{-1}Φ + Γ^{int} [Φ]$$
we can show that the full propagator is given by
$$G= i[iG − Σ]^{-1}$$
With
$$Σ=-Γ_{ΦΦ}^{int} [Φ]$$
Here $Γ_{...
1
vote
0answers
204 views
Question about Gluon self-energy diagram/symmetry factor
I am a qft beginner and have a question:
In Peskin & Schroeder chapter 16.5 there is given an expression for a gluon self energy diagram:
According to the feynman rules we get
$$\frac{1}{2} \int ...