All Questions
Tagged with quantum-electrodynamics self-energy
40
questions
-3
votes
1
answer
100
views
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:
$$ \Pi_2^{\mu \nu} = \frac{-2 e^2}{(4 \pi )^{d/2}}(p^2g^{\mu\nu}-p^{\mu}p^{\nu})\Gamma(2- \frac{d}{2}) \mu^{4-d} \...
- 317
3
votes
1
answer
130
views
Weisskopf and self-energy
I am working my way through the 1934 paper by Weisskopf on the self-energy of the electron and is much helped by the English translation found here. I do have some difficulties with section 2 of this ...
- 91
1
vote
0
answers
72
views
Confusion about the dressed propagator
When considering interactions, the free propagator $S_0(p)$ of fermions for example gets "dressed" due to the self-energy of the fermion. The complete propagator then becomes
$$
S(p)=\frac{/\...
- 172
1
vote
0
answers
65
views
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 ...
- 534
1
vote
0
answers
107
views
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:
$$V(p^2)= \frac{e^4_R}{2\pi^2p^2} \int_0^1 x(1-x)\ln[1-\frac{p^2}{m^2}x(1-...
- 11
0
votes
1
answer
217
views
Coupling renormalization $\lambda\phi^4$ vs QED
I have some doubts regarding the allegedly different procedures used in $\lambda\phi^4$ and QED.
First of all, I am more familiar with bare perturbation theory (no counterterms), so I would be ...
- 1,989
5
votes
1
answer
247
views
Radiative correction of the electron self-energy
In Mandl & Shaw's Quantum Field Theory (2nd edition p217), the radiative correction for the electron self-energy is:
$$
e_0^2 \Sigma(p) =
\frac{\tilde{e_0}^2}{16\pi^2} (p\!\!/ -4m) \left(\frac{2}{\...
- 138
3
votes
0
answers
84
views
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 ...
- 61
6
votes
0
answers
167
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 ...
- 3,992
3
votes
0
answers
131
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
$$m^2-m_0^2-\operatorname{Re}...
- 2,122
2
votes
1
answer
153
views
Why is it necessary to use dressed single particle Green's function in QFT bound state problem (Bethe–Salpeter equation)?
On p. 333 in book Quantum Electrodynamics by Walter Greiner, Joachim Reinhardt or other references, they claim that in Bethe–Salpeter equation, we have to use dressed single particle Green's function, ...
- 53
0
votes
2
answers
201
views
Two question about evaluate electron self-energy in Peskin & Schroeder Book Charpter 7.1
(I attached the e-book link beneath)
First question is on P.220 the equation (7.27):
$$\delta m=m-m_0=\Sigma_2(p\!\!/=m)\approx\Sigma_2(p\!\!/=m_0).\tag{7.27}$$
Why taking $\Sigma_2(p\!\!/=m)\approx\...
2
votes
2
answers
440
views
Exact propagator - 1PI diagrams
Above diagram can be written in terms of series:
$$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{...
- 3,474
3
votes
1
answer
482
views
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_{\...
5
votes
4
answers
1k
views
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?
- 115