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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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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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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583 views

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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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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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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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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53 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) \\ \...
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83 views

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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1answer
175 views

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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125 views

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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40 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} \...
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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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163 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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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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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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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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Tadpoles and photon self-energy in QED

Tadpoles diagrams are zero in QED for many reasons, one of them is the Lorentz invariance of the vacuum expectation value of the current. Without considering the external photon line (as Peskin &...
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18 views

In electron transport calculations, should lead self-energies always be diagonal in a mode energy eigenbasis?

In electron transport calculations for semiconductor devices, the non-equilibrium Green's function method is often used. The Green's function takes the form $$G = \left[EI-H-\Sigma_L-\Sigma_R\right]^{-...
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How to calculate the Fock exchange interaction self-energy of a system in momenttum space

I have a Hamiltonian in the momentum space which has a strong non-local electron-electron interaction. I know that I have to find its corresponding exchange self-energy and solve the Dyson equation ...
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How to find the functional self-energy?

I have a system with $e$-$e$ interaction. After using the mean field approximation, my Hamiltonian has the following form: $H = H_0 + H_I$, which $H_0$ is the non-interacting and $H_I$ is the ...
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How to calculate thermal corrected masses of Higgs and Gauge bosons?

How are the self energies of scalars and gauge bosons at finite temperature calculated in the process of determining the 1-loop resummation of Debye masses? I have seen some papers where the explicit ...
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86 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 ...
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Deriving relation between pole and running quark masses

How do I compute quark self energy and use it in order to derive detailed relation between pole and running quark mass? If I do it for one loop, I should use this for running mass: $\mu^2\times\...
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39 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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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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746 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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1answer
40 views

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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828 views

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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701 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 ...