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.
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Is there a $k$-space representation of a semi-infinite lead?
An infinite lead has a Hamiltonian of the form
$$\begin{bmatrix}\ddots\\\\&&\beta^\dagger&\alpha&\beta\\&&&\beta^\dagger&\alpha&\beta\\&&&&\beta^\...
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Why don't (electrically charged) particles act on themselves?
As per the Maxwell-Gauss equation, an electron modifies the electrical field around it. Therefore it should act (through an electric force) on itself. Now obviously this force would be directed ...
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Self-energy of a spin 1/2 particle
I want to calculate the self-energy of a spin 1/2 particle. This spin 1/2 particle (a nucleon) has in the self energy loop a nucleon and a pion.
We can write the propagator at the tree level as
$$ \...
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$\log{(4 \pi)}$ in dimensional regularization integral for vacuum polarization
I have been reading through Peskin's chapter 7 and I have arrived at this expression for the first order correction to the photon propagator. Peskin uses dimensional regularization and even though I ...
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Exact propagator - 1pI diagrams
Above diagram can be written in terms of series:
$$i\Delta = -\frac{i}{p^2 + m^2} + \Big(-\frac{i}{p^2 + m^2}\Big)(i\Pi)\Big(-\frac{i}{p^2 + m^2}\Big)+ \Big(-\frac{i}{p^2 + m^2}\Big)(i\Pi)\Big(-\frac{...
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Resummation of single class of diagrams vs all 1PI diagrams
In the book A Modern Introduction to Quantum Field Theory, Maggiore considers the resummation of tadpole diagrams as its own individual geometric series to give
$$\frac{i}{p^2-m^2-B}\tag{1}\label{1}$$
...
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Gravity's self-energy
Suppose we have a single massive point particle.
In the absence of "potentials", the content of the stress-energy tensor would be dictated uniquely by the particle's mass and trajectory (...
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Matrix elements of the self-energy in the GW approximation
I have been teaching myself the $GW$ approximation (or the $G_0W_0$ version of it). I am able to follow the entire derivation of Hedin's equations, etc. and the $GW$ approximation itself. However, I ...
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Is the 1PI self-energy of a massive photon transverse? EDIT: Upsetting consequences for the photon mass and renormalizability
Suppose we had the Lagrangian:
$$\mathcal{L} = -\frac{1}{4} F^{\mu \nu}F_{\mu \nu} + \overline{\psi} (i \gamma^{\mu}\partial_{\mu} -m)\psi -e\overline{\psi} \gamma_{\mu} \psi A^{\mu} +\frac{1}{2} m_{\...
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What does 't Hooft mean by "integrating symmetrically"?
I always wanted to understand what re-normalization in particle physics really means. Having a background in statistical physics I do understand it in there but as far as I know re-normalization in ...
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Is self-energy $\mathrm{Im}\Sigma^r<0$ always true?
Consider a one-particle retarded Green's function $$G^r(\alpha)=[\omega+i\eta-\varepsilon(\alpha)-\Sigma^r(\alpha)]^{-1}$$ with self-energy $\Sigma^r(\alpha)$ for some quantum number $\alpha$. It is ...
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Vacuum polarisation in QED - why is it significant to renormalisation?
I have followed along for the derivation of the amplitude of the 2-photon vacuum polarisation and the book says the result is important for the renormalisation of QED, why is this?
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How many different diagrams contribute to the two-photon amplitude in QED?
I can only think of this particular diagram, though there must be more as I believe the amplitude is supposed to be equal to 0, as it is used to highlight renormalisation in QED.
Which other ...
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Fock Diagram Self-Energy with the Hubbard Model
I am dealing with the Hubbard model and I am wanting to compute the self-energy of this Fock diagram, in the case of the Hubbard Model.
I understand the expression from this diagram could be listed as:...
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Why is vacuum polarisation diagrams called like this?
I have read about the vacuum polarisation diagrams e.g. for the photon propagator, but I don't understand why it is called "vacuum polarisation". Can it be interpreted as an interaction of ...
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Is the electron a pointlike particle? And if yes, how is that possible, because the energy then would diverge, wouldn't it?
My problem is that I read (besides others in this post Why are electrons and quarks 0-dimensional?) that the electron is a point-like particle. My question is on the one hand whether that is true and ...
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Approximate analytic ways to obtain self-energy diagrammatically
I am working on a problem that involves calculating a series of Feynman diagrams for the self-energy. In Dyson's equation, assuming a time independent Hamiltonian:
\begin{eqnarray}
G(i\omega_{n})=G_{0}...
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What is, diagrammatically, the 2-vertex $\Gamma^{(2)}$?
I know that the 2-vertex $\Gamma^{(2)}$ is the second derivative of the effective action, but I fail to see what it is diagrammatically: is it the truncated 1PI diagram? The non-truncated one?
If this ...
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Self-energy of solid hemisphere
I am trying to find the self energy of a solid uniform hemisphere of mass $M$ and Radius $R$ by taking elemental rings with 2 parameters to find gravitational potential at the curved surface but end ...
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Do Tadpoles Contribute to Self-energy?
In evaluating contributions to the two-point function in say $\phi^3$ theory to:
$$\langle 0|\phi(x)\phi(y)e^{-i\int d^4z\frac{\lambda}{3!}\phi^3(z)}|0\rangle,$$
at $\mathcal{O}(\lambda^2)$, one of ...
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Choosing the positive infinitesimal in plotting the spectral function
In a recent project I have been working with spectral functions as a way to find quasiparticle energies, and I have a (perhaps rather naive) question. So let's say that we have single particle ...
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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 ...
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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 ...
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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 ...
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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, ...
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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 ...
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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 ...
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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-...
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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 ...
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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 ...
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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
$$ V(q, i\...
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Dimensional analysis and more: Order of divergences in the $\phi^4$ theory
On page 324 of his book on qft, Peskin analyzes the superficial degree of divergence of the 1-loop self-energy correction of the $\phi^4$ scalar theory. Realizing that $D=2$, he concludes that the ...
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Gauge invariance of loop Diagrams
Say we have a gauge-fixed QED Lagrangian: $$\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.$$
My question ...
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What are the sources of infinities in (unrenormalized) quantum field theory calculations?
The PSE questions and answers about this question I've found don't answer it to my satisfaction, so I am asking my own version, with the principal options I am aware of listed. Although one ...
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From 1PI function to cross section
The full propagator in QFT is the inverse of this two-point 1PI function defined as $$
\tilde{\Gamma}^{(2)}(p)=p^{2}-m^{2}-\Sigma(p)
$$
where $\Sigma(p)$ is the self-energy. I am have calculated the ...
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QCD quark self-energy, is the propagator momentum in the right direction?
For the quark self-energy diagram the amplitude is giving by:
The fermion propagator is given by $\frac{i}{\not p + l}$ in the lecture. It is not supposed to be $\frac{i}{\not p - l}$? It's seems ...
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Does a vanishing self-energy imply a Gaussian fixed point in a $\phi^4$ theory below the upper critical dimension?
Assuming a QFT description of a second-order phase transition. From the free theory, one obtains some critical exponents and one performs an $\epsilon$-expansion below the upper critical dimension. ...
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How can the connected Greens 2pt function be summed as a geometric series of the self-energy if the self-energy contains divergent terms?
In Ryder's book on QFT page 341 we can see
$$\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}$$
and hence putting $D_{\mu\...
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How to derive $\imath q^\mu\mathcal{M}_ \mu(k;q;p)=0$?
\begin{equation}
\imath q^\mu\mathcal{M}_ \mu(k;q;p)=-\imath\tilde{e}\mathcal{M}_0(p;k-q)+\imath\tilde{e}\mathcal{M}_0(p+q;k)
\end{equation}
This is exactly the Ward-Takahashi identity for two ...
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Dimensional regularization of Electron self-energy from Ryder's book
I am Studying Electron self-energy using Ryder's textbook, In page 334 we can see
Defining $k'=k-pz$ and avoiding the term linear in $k'$(because it integrates to zero) gives
\begin{equation}
\Sigma(...
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Why we insert self-energy subgraphs in external lines to cancel infrared divergences completely (like in QED)?
Here we need to keep terms originating from the same line.
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Is it correct this formula for electrostatic energy?
In CGS: I know that:
$$
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})\...
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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 $\...
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Self-energy of a $D$-dimensional statistical mechanical model
We consider a $D$ dimensional statistical mechanical model whose partition function is given by
$$\begin{aligned}
\mathcal{Z} &=\int \mathcal{D} \phi(x) \exp \left(-\mathcal{S}_{\phi}\right) \\
\...
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Scalar self-energy in $\mathcal{N}=4$ SYM in position space
In this paper (BMN Correlators and Operator Mixing in $\mathcal{N}=4$ Super Yang-Mills Theory, 2002), the authors give the following expression for the self-energy of the scalar propagator in $\...
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One-loop diagram self-energy
I need to find the diagram contributing to the self energy of $\varphi$. Say I had an interaction term in the Lagrangian 2 $\varphi$ real scalar fields, and one $\psi$ real scalar field, $\varphi^2\...
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Iterative Greens function calculation
I have a Hamiltonian which has an interactive and non-interactive parts.
$H = H_0 + H_I$
$H_I$ comes from the non-local electron-electron interaction and must be calculated self-consistently.
I ...
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Why is the self-energy for quarks in $d=2$ Large $N$ QCD only order $g^2$?
In an interesting article by 't Hooft , he is able to find the exact quark propagator, in the large $N$ limit of QCD. He finds that the full 1PI self-energy is given by:
$$\Gamma(p)=-\frac{g^2}{2\pi} \...
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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 ...
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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 ...
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