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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Coupling renormalization $\lambda\phi^4$ vs QED
I have some doubts regarding the allegedly different procedures used in $\lambda\phi^4$ and QED.
First of all, I am more familiar with bare perturbation theory (no counterterms), so I would be ...
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Pauli-Villars regularization and self-energy
In the calculation of the electron self-energy in QED (one-loop level), there is a UV and IR divergent integral that needs to be regularized. A common choice for the regularization is the Pauli-...
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Product of delta functions in fermion self-energy at finite temperature
In the calculation of the fermion self-energy at finite temperature, there seems to be a term containing the product of two delta functions which when combined equal zero, however I fail to see why ...
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Radiative correction of the electron self-energy
In Mandl & Shaw's Quantum Field Theory (2nd edition p217), the radiative correction for the electron self-energy is:
$$
e_0^2 \Sigma(p) =
\frac{\tilde{e_0}^2}{16\pi^2} (p\!\!/ -4m) \left(\frac{2}{\...
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Fermion mass correction always proportional to it's mass? even in case of mixing?
In QED, it is obvious that one-loop correction to the mass of the fermion ($\psi$) is proportional to its bare mass. However, it is not very clear to me whether it is general even in the case when ...
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Why does it make sense to do Dyson Resummation with first-order 1PI-diagrams?
This is somewhat related to This question.
The way I understand renormalisation (e.g of the mass) is that we consider the loop-corrections order by order in the coupling constant. If we then consider ...
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Dielectric (and non-dielectric) Electrostatic Energy - some possible misconceptions and interpretations
Suppose one is given with a system of charges, and is tasked to find the work it takes to build it, in a purely electrostatic situation. Microscopically, it is clear the answer is simply:
$$\iiint \...
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Nonequilibrium green function for interacting systems
In this book by Ryndyk on quantum transport, p. 89, the retarded single-particle nonequilibrium Green function for a non-interacting nanosystem coupled to semi-infinite reservoirs of non-interacting ...
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Weinberg Vs Srednicki analysis for the electron self-energy
I am reading Srednicki's book on QFT. Specifically, I am reading about the loop corrections to the fermion propagator (Chapter 62). The relevant expression representing the one-loop and counterterm ...
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Electrostatic potential energy of a conducting polo
Consider a thick metallic sphere with inner radius R1 and outer radius R2 . Now charge q2 is given to the conductor and another charge q1 is held fixed at the centre. How do we calculate the ...
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Gauge invariance and Ward Identity?
I have to work on vacuum polarization and gauge contributions for a given problem.
I have to compute and show that their sum is gauge invariant, which according to the exercise, is equivalent to ...
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Doubt regarding the work done by macroscopic electric fields
Suppose I have a large collection of microscopic charges, say $10^{30}$ or so, occupying some large 3d space. I want to find the work it takes to build this collection.
In an ideal world, one would ...
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Energy in reconfiguring a system of charges
Let's all agree that the formula $ \frac{1}{2} \iiint \rho_{macro} V_{macro} d\tau $ is a decent approximation to the work done to build this system of charges (basically a considerably large charge ...
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Doubt regarding the macroscopic version of the electrostatic energy
Some caveats before you start reading:
The averaging procedure I subscribe to when bringing out the macroscopic Maxwell's equations from the microscopic ones(to a decent approximation in preserving ...
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Unstable particle problem in Peskin and Schroeder
I'm confused by the meaning of the field strength renormalization on page 237 of Peskin and Schroeder. In it, they define the physical mass $m$ of the unstable particle by
$$m^2-m_0^2-\operatorname{Re}...
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Gauge boson self-interaction diagrams
On page 522 of Peskin and Schroeder, we try to calculate the self-energy of gauge boson. Figure 16.7 gives the following diagrams:
However, Peskin and Schroeder says there are three additional ...
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While calculating self-energy or work required to assemble a continuous charge distribution, do we take the energy of an element with itself?
while calculating the self-energy of a continuous charge distribution using the formula
the potential $V$ here is due to the whole charge distribution but we need potential due complete charge ...
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Why do we insist that the electron be a point particle when calculation shows it creates an electrostatic field of infinite energy?
I've heard compelling reasons to think that it is one although why do we assert this in light of the calculation which shows a point particle creates an electrostatic field of infinite energy (see e.g....
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Why is it necessary to use dressed single particle Green's function in QFT bound state problem (Bethe–Salpeter equation)?
On p. 333 in book Quantum Electrodynamics by Walter Greiner, Joachim Reinhardt or other references, they claim that in Bethe–Salpeter equation, we have to use dressed single particle Green's function, ...
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Expansion of IR Divergent integrals
I'm reading this paper about QED counterterms:
https://southampton.ac.uk/~doug/qft/aqft3.pdf
In this paper by calculating the electron self energy we have following expression:
$$\Sigma(p^2,m) = -\...
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Missing term in first-order energy of an homogeneous electron gas?
For jellium, the electron-electron interaction energy of a homogeneous electron gas is
$$V=\frac{e^2}{2\mathcal V}\sum_{\sigma\sigma'}\sum_{\mathbf q}\sum_{\mathbf k \mathbf k}\int\mathrm{d}^3\mathbf ...
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Holographic self-energy for a scalar field in a slice of AdS
I am confused about a key step in Gherghetta's "TASI Lectures on a Holographic View of Beyond the Standard Model Physics" in the derivation of the holographic self-energy in the strongly ...
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The proper self-energy diagrams for the Anderson model
According to Fetter's book, the Feynman diagrams contribute to the proper self-energy are:
where the first and second orders here refer to the perturbation expansion of the interacting Green's ...
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How can the mass of an unstable composite particle become complex?
To show where the resonances in cross sections come from, one usually considers the exact propagator in the interacting theory, which for a scalar is
$$iG(p^2)=\frac{i}{p^2-m_R^2+\Sigma(p^2)+i\epsilon}...
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Do unresummed self-energy functions spoil RGE resummation?
I am aware, that the solution of the $\beta$-function contains a resummation of all large logarithms, but I fail to understand how this is actually relevant: The coupling constant is not an observable ...
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Renormalization constant in unstable particle propagator
On Peskin & Schroeder's QFT, section 7.3, the book discusses the unstable particle.
Before (7.57), the book gives the formula of a scalar particle propagator
For unstable particle, the book ...
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Feynman diagrams related to Hedin's equations and OEIS A286784
OEIS A286784 contains the lower triangular matrix
1;
1, 1;
2, 4, 1;
5, 15, 9, 1;
14, 56, 56, 16, 1;
... ,
with elements $T_{n,k}$ (initialized with $n=k=0$) which ...
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From which interaction term does the self-energy diagram of $\phi^4$ theory come?
In 4D, let us start with the normal-ordered product of free neutral scalar fields $:\phi^4:$.
Then, we can in fact write $$:\phi^4:=\sum_{i=0}^4 V_i$$ where each $V_i$ is an operator-valued ...
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Two question about evaluate electron self-energy in Peskin & Schroeder Book Charpter 7.1
(I attached the e-book link beneath)
First question is on P.220 the equation (7.27):
$$\delta m=m-m_0=\Sigma_2(p\!\!/=m)\approx\Sigma_2(p\!\!/=m_0).\tag{7.27}$$
Why taking $\Sigma_2(p\!\!/=m)\approx\...
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On-shell renormalization (Schwartz Quantum Field Theory Equation (18.48))
I have a question about how, in section 18.3.2 in Schwartz's quantum field theory, he goes from equation (18.47) to (18.48) using Pauli-Villars regularization. It comes down to showing that to leading ...
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Fermion self-energy and vertex renormalization in Non-Abelian Gauge Theories
I am currently going through chapter 16 of Peskin and Schroeder and some of the calculations seem very obscure to me. The problems are as follows:
On page 528, the authors compute the value of the ...
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Electron Self-Energy
Suppose an electron is bound to a nucleus, leading to an overall charge density
$$
\rho(x) = Ze\delta(x) - e \left|\psi(x) \right|^2.
$$
If I interpret this charge density just as I would in the ...
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What is an example of a massless field that acquires a mass from quantum corrections?
It's all in the title. In eq. (7.75) of Peskin they say the full photon propagator takes the form
$$\frac{-i\ g_{\mu\nu}}{q^2 (1- \Pi(q^2))}\, \tag{1}$$
and that the photon remains massless as long as ...
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What is the self-energy, and what are the vertex corrections? [closed]
In the paper I am reading, they said
"If we want to evaluate a transport coefficient, in a typical situation the single-electron self-energy is not sufficient: one needs to know vertex ...
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Infrared divergence in electron self-energy
On Peskin and Schroeder's QFT book, page 319, the book discussed various situations of QED divergence.
On the first paragraph of p.319, the book considered Taylor series of electron self-energy ...
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A question about the contraction in the calculation of gauge boson self-energy
I'm studying the chapter 16 of Peskin and Schroeder's An Introduction to Quantum field theory and I don't quiet understand the contraction rule used in this chapter. For example, for eq(16.63) $$\frac{...
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Corrections to self-energy/radius of an electron due to gravity [closed]
I am currently reading Feynman's lectures on electromagnetism, and the question of the electrons self-energy, its size, and "what keeps it together" are mentioned in several places.
Now I ...
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Different answers for self-energy?
If we calculate the self-energy using the energy density integral then we get
$$U=\int^\infty_0\frac{q^2}{8\pi\epsilon_0 r^2}dr=-\frac{q^2}{8\pi\epsilon_0 r}$$
However, since the potential of a point ...
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Mass renormalization of the Schwinger model
If there are no divergent diagrams in the self-energy, is the bare mass equal to the renormalized mass in the continuum limit Schwinger model with 1 flavour in 1+1 dimensions?
Let $m_r$ = renormalized ...
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Peskin and Schroeder p. 409 “quadratically divergent mass renormalization”
I have three questions about page 409 of Peskin and Schroeder.
First, they state that the diagram
where $\Delta = m_f^2 - x(1-x)p^2|_{m_f=0}$, has a pole at $d=2$ “corresponding to the quadratically ...
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Why don't (electrically charged) particles act on themselves?
As per the Maxwell-Gauss equation, an electron modifies the electrical field around it. Therefore it should act (through an electric force) on itself. Now obviously this force would be directed ...
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Exact propagator - 1PI diagrams
Above diagram can be written in terms of series:
$$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
Maggiore considers on page 136 in Section 5.6 Renormalization in the book A Modern Introduction to Quantum Field Theory, the resummation of tadpole diagrams as its own individual geometric series to ...
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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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