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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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Loop Effect of $\phi$ Propagator in $t$-channel of scalar $\phi^3$ theory [closed]

In Schwartz's QFT chapter 16, he calculates the loop effect (vaccum polarization) of $\phi$ propagator in $\phi^3$ theory, with the choice of Pauli-Villars regulator, the scattering amplitude would be ...
Ting-Kai Hsu's user avatar
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Some calculation in Schwartz's Quantum field theory eq. (16.39)

In Schwartz's Quantum field theory and the standard model, p.307 he derives a formula: $$ \Pi_2^{\mu \nu} = \frac{-2 e^2}{(4 \pi )^{d/2}}(p^2g^{\mu\nu}-p^{\mu}p^{\nu})\Gamma(2- \frac{d}{2}) \mu^{4-d} \...
Plantation's user avatar
1 vote
2 answers
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Understanding Feynman Diagrams in Loop Corrections to the propagator $\phi ^3 $ theory [closed]

I found other posts talking about the same chapter in the same book, but none of them were exactly about what I am asking here. In Srednicki's chapter 14 (Loop corrections to the propagator), we are ...
Fernando Garcia Cortez's user avatar
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Weisskopf and self-energy

I am working my way through the 1934 paper by Weisskopf on the self-energy of the electron and is much helped by the English translation found here. I do have some difficulties with section 2 of this ...
Trond Saue's user avatar
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Self-Energy of a Conducting Shell based on Surface Charge Distribution

If a charge $q$ is given to a shell of radius $r$ (conducting or non-conducting) it's self-energy is $kq^2/2r$, $k$ being Coulomb's constant. But if the shell is conducting and the charge on the inner ...
JustAMathsGuy's user avatar
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Determining if Self-Energy is Complex from Action Alone?

My understanding of quantum field theory is that an interacting two-point function of spin-0 bosons will have the form: $ \frac{i}{p^2-m_0^2-\Sigma(p)}$, where $\Sigma(p)$ is the self-energy, the sum ...
JudahReynolds's user avatar
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Perturbation theory of Anderson impurity model

I’ve been learning about DMFT(Dynamical mean field theories) these days and have encountered rather simple questions in many-body perturbation theory. It is about IPT Impurity solver (applying ...
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Exact definition of topological non-identical diagrams

It is often said that Feynman diagrams for fermions do not have symmetry factors. Consider I have a spinless fermionic quantum many-body system with Hamiltonian: $$H=\int_{r}\psi^{\dagger}(r)\frac{\...
John 's user avatar
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Renormalization in Background field gauge

The purpose of this question is not very straightforward to explain. So, I just state the question. If we use Background field gauge for renormalization, due to the QED-like Ward identities, the ...
Tanmoy Pati's user avatar
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Electric potential energy, Electric potential and self-energy of a body

The total work done to bring all the charges constituting a body from infinity to the body one by one is called the electrostatic potential energy of the body. And if I divide the expression of ...
Peter swift's user avatar
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Relation between Dyson equation, Kadanoff-Baym equations and 2PI formalism

I am learning the framework of non-equilibrium field theory. Probably this is clear enough to an expert, but the expansive number of formalism, methods, and frameworks is confusing for a beginner. I ...
ds283's user avatar
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Electrostatic Self-energies of Non-uniformly charged bodies

Consider the figure given above. A semicircular ring of radius $R$ and mass m carries non uniform linear charge density $λ=λ_o\sin\theta$. A rod of mass $m$, length $2R$ and uniform linear charge $λ_o$...
DarkKnight's user avatar
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1 answer
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Understanding $W^{(n)}$, $\Gamma^{(n)}$, and $\Sigma$ in Feynman diagrams

In quantum field theory (specifically $\phi^4$ theory), $W$ is the sum of all connected Feynman diagrams and the effective action $\Gamma$ is the sum of all 1PI Feynman diagrams. They are related by a ...
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Renormalization condition for field strength renormalization

I am studying $\phi^4$ theory and so far I understand the mass and coupling constant renormalizations. In these theories, once we expand a diagram in perturbation theory we "cancel" the ...
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How does the on-shell (OS) scheme work if we assume mass to be zero?

When calculating the self-energy correction of a massless quark up to one loop, I get $$i\Sigma(p)=i\frac{\alpha_s}{4\pi}C_F/\!\!\!{p}\left[\frac{1}{\varepsilon_{\text{UV}}}-\gamma+\ln(4\pi)+1+\ln(\...
Ozzy's user avatar
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Confusion about the dressed propagator

When considering interactions, the free propagator $S_0(p)$ of fermions for example gets "dressed" due to the self-energy of the fermion. The complete propagator then becomes $$ S(p)=\frac{/\...
Ozzy's user avatar
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Do quark self-energy insertions on external quark lines vanish in the MS scheme?

As far as I know, if one wishes to consider quark self energy diagrams inserted on external legs of a scattering amplitude, they cancel with the crossterm diagrams in the on-shell scheme. For this ...
Ozzy's user avatar
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Mass, field renormalization in QED

I am trying to understand the formula for mass and field renormalization in QED from the book Gauge theory by Bohm, Denner, pp $202$. They use renormalized perturbation to rewrite the Lorenz gauge ...
Tanmoy Pati's user avatar
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Self-energy of a spinon coupled to a $\rm U(1)$ gauge field

I would like to understand how to calculate the 1-loop self-energy for spinons coupled to a $\rm U(1)$ gauge field. For context, I am going through Nagaosa & Lee's "Gauge theory of the normal ...
dumbpotato's user avatar
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Keldysh contour and time-dependent observables

How to use the non-equilibrium Keldysh Green's function to solve a driven harmonic oscillator? A quantum harmonic oscillator $H_0 = \omega_0 a^\dagger a $ is coupled to a pump field E(t) (refer to ...
vcuteym's user avatar
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About On-shell subtraction and renormalization

I really want your help, i have tried to solve it for two days but I couldn’t, therefore if you could help me by giving guidance and hint, i really appreciate it. My question is that how to perform ...
Roden's user avatar
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What is the difference between interaction energy and self-energy?

From my understanding self-energy is the energy required to put charges in a certain charge distribution and interaction energy is the potential energy caused by the interactions between particles, ...
randomdude's user avatar
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One-loop potential correction in QED (Lamb shift)

Vacuum polarization 1-loop in QED gives another term in potential, named Lamb shift. Potential in terms of momentum $p^2$ is: $$V(p^2)= \frac{e^4_R}{2\pi^2p^2} \int_0^1 x(1-x)\ln[1-\frac{p^2}{m^2}x(1-...
Fairy's user avatar
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One-loop renormalization of $\phi^4$ theory in Cheng and Li

In Gauge Theory of Elementary particle Physics by Cheng and Li, They manipulate the self-energy 1PI vertex as I am quite confused how one gets (2.20), what type of expansion is this?
realanswers's user avatar
1 vote
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Pedagogic Notes on graviton self-energy 1-loop Calculation

Any lecture notes on graviton self-energy 1-loop calculation would be appreciated. A detailed account of how to calculate the vertices of three gravitons, how to assign the momenta with signs to the ...
0 votes
1 answer
106 views

Kinetic mixing, and a bare mass?

I've been reading the following classic paper by Bob Holdom "Two $U(1)$s and $\epsilon$ charge shifts", and I'm attempting to derive the expression for $\chi$. In particular, I am computing ...
Guy's user avatar
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0 votes
1 answer
210 views

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 ...
Mr. Feynman's user avatar
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2 votes
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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-...
Mr. Feynman's user avatar
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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 ...
justsome1's user avatar
5 votes
1 answer
246 views

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}{\...
nomeruk's user avatar
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3 votes
0 answers
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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 ...
PhysicsStudy's user avatar
2 votes
1 answer
184 views

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 ...
Lenard Kasselmann's user avatar
1 vote
0 answers
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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 \...
nickbros123's user avatar
1 vote
0 answers
80 views

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 ...
Rudolf Smorka's user avatar
6 votes
0 answers
166 views

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 ...
schris38's user avatar
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1 answer
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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 ...
aman jain's user avatar
2 votes
0 answers
83 views

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 ...
god_operator's user avatar
2 votes
1 answer
119 views

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 ...
nickbros123's user avatar
0 votes
1 answer
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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 ...
nickbros123's user avatar
0 votes
2 answers
91 views

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 ...
nickbros123's user avatar
3 votes
0 answers
129 views

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}...
Ghorbalchov's user avatar
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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 ...
Simplyorange's user avatar
0 votes
1 answer
33 views

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 ...
Khushank's user avatar
6 votes
6 answers
3k views

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....
greatscissors's user avatar
2 votes
1 answer
151 views

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, ...
swish47's user avatar
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1 vote
0 answers
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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) = -\...
Monterosa2's user avatar
1 vote
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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 ...
Mauricio's user avatar
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1 vote
1 answer
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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 ...
Henry Deith's user avatar
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4 votes
1 answer
288 views

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 ...
Bekaso's user avatar
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7 votes
3 answers
953 views

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}...
F.Burton's user avatar
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