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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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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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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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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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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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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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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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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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 \...
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302 views

Diagrams involved in 1-loop electron self-energy in QED

I'm following the derivation of electron self-energy at 1-loop in QED on Peskin-Schroeder, page 216. To second order in the coupling the considered diagram (7.15) is The 2-point correlator at second ...
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Where are the poles of the one-particle Green's function located in the complex plane?

This post is a followup question to: How to get an imaginary self energy? In the cited post, the two following representations for the one-particle Green's function are shown: $$G(k,\omega) = \...
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Infrared cutoff in the Kramers-Kronig relation for the marginal Fermi liquid

I am going through Andre-Marie Tremblay's derivation of the real part of the self energy in his lecture notes on the many-body problem. On page 254, if we take the imaginary $\Sigma''(k,\,\omega)\sim \...
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Asymptotic relation of Green's function for diverging self energy

I am considering the derivation on pages 64 to 66 of Zagoskin's Quantum Theory of Many-Body Systems. They consider a Green's function in the Lehmann representation: $$ G(p,\,\omega)=(2\pi)^3 \sum_s \...
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Integrals involving Bose-functions (Computational)

In short, I'm looking for some advice/literature how to deal numerically with Bose function. My physical problem is to calculate a coupled set of Self-energies, thermal loop integrals, self ...
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Why electron self-energy and other processes like vacuum polarization is not possible classically? [closed]

Why electron self-energy and other processes like vacuum polarization is not possible classically?
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One-Particle Self-Energy (Yang-Mills)

I've been asking about an interesting question when i was calculating the self energy of a Gauge boson in Yang-Mills theory. I think that the correct way to think this problem is: the incident ...
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If 2 particles produce a potential equal to $\frac{k}{r}$ for each position $r$, how can I deal with the infinities from self-energies?

Sorry if the title is a bit floppy. I am studying two particle systems and their energy. I was given that (equation 1): $$\mathbf F=-\mathbf \nabla U.$$ For a potential $U$, which is the same for ...
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Is Ward identity really satisfied by the photon's self energy?

The one-loop self-energy of the photon, , when contracted with the external momentum $k^\mu$ gives the following difference of integrals where the integration variable in the first term is shifted ...
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How do we decide the perturbation term in the Hamiltonian and what's the difference for the self-energy due to different perturbation terms?

The final result of many-body perturbation theory based on Green's function method can be organized into the famous Dyson equation: $$G = G_0 + G_0 \Sigma G=G_0 + G \Sigma G_0 \tag{1}$$ where $G/G_0$ ...
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Deriving relation for gravitational self energy

My book says $U_{self}=\dfrac{-GM^2}{2R}$ for the hollow sphere, I tried deriving it as: Suppose mass constructed is $m$, Work done on bringing mass $dm$ from $\infty$ to $R$ is $$dW=dm(V_{R}-V_{\...
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The electric field generated by a point charge becomes infinite when distance tends to zero. What physical meaning does this have? [duplicate]

What follows is from Professor Barton Zwiebach of MIT: The only problem with such a large field is an infinite self-energy of the point particle limit. This problem is not really there in QED, as ...
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470 views

Difference Between Vertex Function and Self Energy

I am trying to understand the difference between the 2-point vertex function and the self energy. In many presentations, they are described in ways that seem nearly equivalent, yet as I work through ...
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543 views

Analytical expression for Hartree-Fock diagram

The picture above is taken from "introduction to many-body physics" by Coleman. When I try to write down the momentum space expression for the two diagrams, I got the same expression for the first one,...
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How to correctly understand these “1-particle-irreducible insertions”?

In QED, when dealing with the vacuum polarization and the photon propagator, some authors like Peskin & Schroeder introduce the so-called "1-particle irreducible" diagrams. These are defined as: ...
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Self-energy of an electron

In his 1947 paper, Bethe states that the self-energy of an electron in a quantum state $m$, due to its interaction with transverse electromagnetic waves is $$W = -\frac{2e^2}{3\pi\hbar c^3}\sum_{n}\...
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Why is it the finite piece of the self-energy often neglected to define the physical mass?

Using the bare perturbation theory, for a $\lambda\phi^4-$theory in $d$-dimensions, the regularized self-energy turns out to be $$\Sigma=-\frac{\lambda_0 m_0^2}{16\pi^2\epsilon}+\text{finite}\tag{1}$$ ...
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Did Feynman ever solve the problem of the difference between bare mass and self-energy of the electron?

The question had to do with the idea that space was filled with particles and that electrons could only exist in specific locations, and same with positrons in the "holes." But if the electron has ...
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How can we use geometric series in calculating Green's function sum over loop effects

I found Greens function summing over repeated insertion of 1PI in Schwartz p.330: $$ \begin{aligned} iG(\not p)&=\frac{i}{\not p-m}(i\Sigma(\not p))\frac{i}{\not p-m}+\frac{i}{\not p-m}(i\Sigma(\...
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Why is the electron self-energy gauge dependent?

Let $\psi(x)$ be the field of the electron. Its Fourier transformed two-point function reads $$ \langle\psi\bar\psi\rangle=\frac{1}{\not p-m-\Sigma(\not p)}. $$ If we calculate $\Sigma(\not p)$, we ...
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On the asymptotics of interacting correlation functions

Consider an interacting QFT (for example, in the context of the Wightman axioms). Let $G_2(x)$ be the two-point function of some field $\phi(x)$: $$ G_2(x)=\langle \phi(x)\phi(0)\rangle $$ Question: ...
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Fermion self-energy

I try to calculate the mass matrix for a massless fermion mediated by a loop of massless (right handed) neutrino and a scalar like the next diagram The amplitude is given by: $$ i M = \bar{u}_{s_i}(...
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How to prove that the spectral line-width is given by the imaginary part the self energy?

I am trying to understand the computational methods to calculate the spectral line-width as done in this paper, http://www.nature.com/articles/ncomms11755 Here, they say that the line-width is ...
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What are the pragmatic solutions to point charge self-force/self-energy in relativistic simulations?

(I'm considering classical relativistic mechanics and classical electrodynamics throughout this post.) Usually, you calculate the motion of charges due to an external electromagnetic field, or you ...
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Self-interacting particles [closed]

Definitely,i feel i have no way to understand this topics or related, what is auto-interacting or self-interacting particles, self energy,self-force, what is a self-interactive effect? It's a broad ...
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Conductance of disordered conductor

I'm struggling with a rather advanced problem. Consider a conductor placed between two leads. The conductor is not completely clean but contains all kinds of impurities. The goal is to find the ...
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769 views

Self-energy of a Fermi liquid

A weakly correlated many-electron system can be viewed in a first approximation as a Fermi liquid, meaning that it behaves similarly to a non-interacting electron gas with renormalized parameters. In ...
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how to construct self-energie diagrams

I am working on self-energie and feynmann diagrams. they are not very easy to get but i think i am starting to understand how it works but of course i am not realy sure.and before going any further i ...
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373 views

Mass of a point charge [closed]

A point charge is defined as an electric charge at a mathematical point with no dimensions(Wikipedia: https://en.wikipedia.org/wiki/Point_particle#Point_charge). Can anything be said about its mass in ...
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563 views

determine the mass of ice that melts during the impact

During a storm, a mass $m = 2 g$ hailstone falls to the ground. Its speed just before coming to ground is $v = 18 m / s$. its speed just after is zero. Assume that the hailstone is pure ice, the ...
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How do I get the amplitude for the one-loop photon self-energy?

I am studying Maggiore's book on QFT and I am stuck in the amplitudes of one-loop corrections in QED. Could someone clearly explain me how do I get the following amplitude from the respective diagram? ...
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Question related to charged concentric conducting shells

There is a charged conducting spherical shell given a certain positive charge.Another larger spherical shell is given the same negative charge.The first shell is now placed inside the second shell so ...
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Does a charged particle propagating in free space have a 'self-energy' like term due to it’s interaction with the fluctuations of the quantum vacuum? [closed]

Does a charged particle propagating in free space have a 'self-energy' like term due to it’s interaction with the fluctuations of the quantum vacuum? (particle-antiparticle pairs popping into and out ...
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Random walk recurrence term and the self-energy

Consider the "first passage problem" A random walk proceeds on a graph of connected points. On this graph, there is one "end" point $j$ meaning that if the random walker lands on this point the ...
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Self energy, 1PI, and tadpoles

I'm having a hard time reconciling the following discrepancy: Recall that in passing to the effective action via a Legendre transformation, we interpret the effective action $\Gamma[\phi_c]$ to be ...