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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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 ...
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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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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 ...
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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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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 ...
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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 ...
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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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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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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\...
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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 ...
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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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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 ...
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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 ...
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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 ...
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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 ...
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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} =...
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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 $G'_0(E)$ ...
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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 ...
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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 ...
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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)...
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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 ...
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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(...
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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 ...
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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 ...
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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 ...
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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 ...
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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 $\text{Im}\big[\Sigma(0)\big] = 0$,...
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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}{...
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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 ...
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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)}...
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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_{...
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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 ...