Questions tagged [quantum-electrodynamics]
Quantum electrodynamics (QED) is the quantum field theory believed to describe electromagnetic interaction. It is the simplest example of a quantum gauge theory, where the gauge group is abelian, U(1).
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Can a consistent theory of electric force exist where charges of equal sign attract each other and charges of opposite sign repel each other?
I am preparing tomorrows lesson about electrostatics and the Coulomb law and wondered the following:
By simple experiments we can show that the electric force can be attractive and repulsive, so we ...
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Basis vectors for quantum electrodynamics
The following unnormalized vectors are solutions to the Dirac equation.
\begin{align*}
u_1&=\begin{pmatrix}E+m\\0\\p_z\\p_x+ip_y\end{pmatrix}
\exp\left(\frac{i\phi}{\hbar}\right)
%
& v_1&=\...
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Why isn’t electric potential energy involved in the calculation of pair production?
When I learned about energy conservation in pair production, we only considered the energy of matter and light. Why isn’t the electric potential involved? Also why isn’t the gravitational potential ...
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Massless QED modified Lagrangian
Consider a massless theory of QED, with Lagrangian
$$\mathcal{L}_{QED}=
-\frac{1}{4}F_{\mu\nu}F^{\mu\nu}+\bar{\Psi}i\gamma^{\mu}\partial_{\mu}\Psi+
e\bar{\Psi}\gamma^{\mu}A_{\mu}\Psi$$
Is there any ...
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Scalar particle Compton scattering using relativistic Lagrangian formulation of electromagnetism
We know that parallel to scalar QED, a common formalism that describes a massive particle coupled to electromagnetism is through a relativistic worldline formalism, which writes
$$\mathcal{S}=\int\ ds\...
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Does the electric charge run differently with energy for electrons and for W bosons?
Do the running with energy of the electron charge and of the W boson electric charge differ or are they the same?
Is there any theoretical or experimental evidence that allows the comparison?
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Feynman rules for scalar QED [closed]
Can i have a derivation for the Feynman rules of scalar QED?
I don't understand the ones i find online such as the one in the link https://canvas.harvard.edu/files/936391/download?download_frd=1&...
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Finding momentum of an electron using quantum mechanics in Fermi's 1932 paper
I was reading Fermi's 1932 paper "Quantum Theory of Radiation". I was able to understand the paper until this particular derivation (which was excluded).
$u_m,u_n$ are the eigen-functions ...
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Spin Operator in Massless QED and bases
I have read Subleading soft dressings of asymptotic states in QED
and perturbative quantum gravity by Choi and Akhoury. I wish to understand something very specific, written in Appendix A.1.2 and A.2....
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What are the fundamental equations of quantum electrodynamics?
I hope this question hasn't already been asked, but I looked and couldn't find a question with a similar title.
It is my understanding that Maxwell's equations and the Lorentz force law form the ...
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Amplitude of the process $q \bar q \rightarrow \tau^+ \tau^-H$
I want calculate the cross section of the process $q \bar q \rightarrow \tau^+ \tau^-H$, where the Higgs takes the $vev$. My question is: if the Higgs takes the $vev$ the amplitude of the process is ...
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Quantum beats as temporal interferences : whats does that mean?
I've already seen the expression "temporal interference" used to designate these "quantum beats"; often to contrast with the "spatial" interference that would be ...
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Frenkel or Tulczyjew-Dixon Condition and QED
What is the physical motivation behind imposing Frenkel's condition,
$$p_{\mu}S^{\mu\nu}=0$$
for an electron of momentum $p$ and spin given by some tensor $S^{\mu\nu}$?
In addition, a direct ...
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Covariant Spin Operator for Massless Fermions
I have been reading the paper The Covariant Definition Of Spin in Relativistic QFT by Hilgevoord and De Kerf, in which the authors derive the spin operator in relativistic quantum theories of free ...
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Radiative corrections for the vacuum polarization
In Vanderhaeghen et al. (Phys. Rev. C 62 025501), the photon propagator modified by the vacuum polarization is
$$
\Pi(Q^2) = \frac{-e^2}{(4\pi)^2} \frac{4}{3}
\left[ \frac{1}{\epsilon_{UV}} -\gamma_E ...
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Electromagnetic field strength tensor fermion couplings
The electromagnetic field strength tensor, $F_{\mu\nu}$, contains the electric and magnetic fields as its components. In that case, would one be able to use $F_{\mu\nu}$ to describe specifically the ...
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A paradox about superselection from algebraic QFT
In N.P. Landsman's review of Haag's Local Quantum Physics (p. 523), he notes the following paradox. Haag shows that in infinite volume, the velocity of an electron obeys a superselection rule, which ...
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Hamilton function of a point charge
In Fermi’s 1932 paper, Quantum theory of radiation, he wrote a “Hamilton function of a point charge in radiation field”
I am not able to get how to derive this equation. I have also looked up at ...
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Can the electron $g$-factor be understood as electrons having roughly twice as much momentum as the Bohr Magneton?
I'm trying to make sure I understand the $g$-factor of the electron, so if my question is flawed please don't just point out my flaws, but help me correct my understanding
If I understand correctly ...
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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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Gordon identity in QED [closed]
To derive Gordon identity
$$ \bar u_2 (q^\mu_1 + q^\mu_2) u_1 = 2m \bar u_{2} \gamma^{\mu} u_{1} + i (q_{1,\nu} - q_{2,\nu} ) \bar u_2 \sigma^{\mu\nu} u_1 $$
we use the relation
$$\gamma^\mu q_\mu u(q)...
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A question on Schwartz's derivation of the Euler-Heisenberg Lagrangian
In Subsection 33.2.2. of Schwartz's Quantum Field Theory and the Standard Model, he starts to derive the Euler-Heisenberg effective Lagrangian by "replacing" the field which is being ...
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Coulomb field from QED
It is well-known how to obtain Coulomb's law in perturbative QED (e.g. the answers to this question on this site). I am trying to understand if there is any reasonable way to give a meaning, within ...
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Why can't we "simply" quantize Maxwell's equations without a Lagrangian to create a quantum theory of electrodynamics?
Useful quantum field theories like quantum electrodynamics (QED) suffer from a litany of problems related to the fact that, at least in their usual Lagrangian formulation, interactions between the ...
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What natural processes are most sensitive to exact value of fine-structure constant?
My intuition (game theory PhD here, no serious background in physics) suggests that of all naturally observable processes protein folding should have the strongest dependence on exact value of $\alpha$...
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Why is there a $u$ in the middle of the feynman diagram for a quark and an antiquark annihilating?
There is a feynman diagram in chapter 2 of Griffiths Introduction to elementary particles, where a pair annihilation is taking place. I am confused as before it was written that internal lines are ...
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Total cross-section for Bhabha scattering
The Bhabha scattering differential cross section is given by
$$\frac{d\sigma}{d\Omega}=\frac{\alpha}{2s}\left(\frac{3+\cos^{2}\theta}{1-\cos\theta}\right)^{2}$$
where $\theta$ denotes the angle of the ...
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Trouble with loop calculations
I was trying to do loop calculation. I have done chapter 6 and 7 of Peskin and Schroeder which deals with one loop correction to electron vertex function and vacuum polarization. But I don't feel very ...
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Antiparticles of spinors
As far as I know, to couple scalar fields with photons, the fields must be complex, and have two degrees of freedom, which explains why the antiparticles exist. In the spinor cases, spinors themselves ...
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What is the interplay between radiation and photon creation?
While trying to provide an answer to this question, a question popped into my mind. When a charge accelerates, is there always a photon associated with that radiation, or multiple photons? For ...
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How exactly does a proton form from quarks? What is the exact sequence and mechanism?
What are the steps that lead to the bonding of two up quarks and one down quark into a proton? For instance, does an up quark "bind" with a down quark in quark-gluon plasma, which then binds ...
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Probability amplitudes in Richard Feynman’s QED [duplicate]
So i’ve been reading Richard Feyman’s book, QED, and in it, he simplifies the idea of how physicists calculate the probability of a photon hitting a certain detector. He lets the magnitude of a vector ...
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Why does light interact with normal matter but not with other light?
Why does light interact with normal matter but not with other light?
Assumptions:
Light does not interact with other light at all.
Light does interact with other matter, i.e reflection/refraction.
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Why did Schwinger [Phys. Rev. 74 (1948) 1439] choose a non-standard form of the Lagrangian density associated with the free electromagnetic field?
This sounds like a science history question, but is not. It is about acceptable forms for the Lagrangian density of electromagnetism. There is also a second question on the distinction between total ...
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Why poles of two-point function corresponds to bound states?
In this article Two-time Green function method in quantum electrodynamics of high-Z few-electron atoms the author has:
Let $\mathcal{G}$ be fourier transform of the green function
$$
\begin{array}{r}
\...
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Are static electric and magnetic fields flows of virtual photons? [duplicate]
Many electromagnetic interactions are modeled as exchanges of a real photons: e.g. an excited electron can relax and emit a photon. Somewhere else, a photon and an electron can interact, "...
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Spin magnetic dipole moment of electron not an invariant with acceleration?
Since the energy of the electron at rest can be calculated by:
$$
E_e=\frac{h c}{ \lambda_e}
$$
where $\lambda_e$ is the Compton wavelength value of the electron at rest, $h$ the Planck constant and $...
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Unitarity of time-evolution operator of Dirac's equation
Let $\Psi(t)$ be state of Dirac's electron in context of Dirac's equation and consider time-evolution operator
$$\Psi(t) = U(t)\Psi(0)$$
is or is not $U$ an unitary (preserving length) operator?
(note ...
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Lorentz invariance
In QED loop renormalization, Lorentz invariance is often used to express the possible momentum-dependence of the propagators.
For example, the propagator corresponding to the fermion loop is
$$ie_0^2 \...
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Radiative correction of the electron self-energy
In Mandl & Shaw's Quantum Field Theory (2nd edition p217), the radiative correction for the electron self-energy is:
$$
e_0^2 \Sigma(p) =
\frac{\tilde{e_0}^2}{16\pi^2} (p\!\!/ -4m) \left(\frac{2}{\...
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Why would energy conservation be violated during interference if a wave function represented multiple photons?
the below paragraph is from Paul Dirac's 'The principles of quantum mechanics'. He argues that representing multiple photons' probability distribution via a single wavefunction leads to energy ...
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Propagator and Ward identity in the $R_\xi$ gauge
The full gauge propagator in the $R_\xi$ gauge is
$$D_{\mu\nu} = \frac{i}{k^2+i\epsilon}\left(-g_{\mu\nu}+\frac{1-\xi}{k^2}k_\mu k_\nu\right).\tag{1}$$
Now if we take $\xi=0$, we get the Lorenz gauge, ...
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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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Solving QED Feynman diagram with one vertex
I'm new to Feynman diagrams and I want to calculate the probability of electron and positron anihilating into one photon to show it is impossible. I know this can be shown easier with special ...
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Resource Recommendation - Charge interaction with electric, magnetic and light fields
I am looking for a good book or review on the treatment of a charged particle interaction (an electron typically) with magnetic, electric and electromagnetic fields. Ideally with both classical and ...
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Minus sign for incoming antifermions
In his Diagrammatica, The Path to Feynman Diagrams (Cambridge University Press, 1994; §4.5 "Quantum Electrodynamics", p. 88), M. Veltman reports the following Feynman rule for incoming ...
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Feynman Chapter 13
I was reading Feynman's lectures on Quantum Mechanics. In chapter 13 he derived the amplitude to find an electron in a 1-D lattice for a stationary state. This amplitude is a pure immaginary number ...
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Having trouble understanding the electric field on the surface of a current-carrying wire
I'm tasked to calculate the electric field on the surface of a wire with current I and voltage U and radius a and length l.
My first instinct was to use Gauss's law:
$\int \vec E \cdot d \vec a = 2 \...
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About Compton scattering in QED
Consider the Compton scattering
$$e^{-}(p,s)+\gamma(k,\lambda)\rightarrow \gamma(k',\lambda')+e^{-}(p',s')$$
To calculate the process' amplitude one has to compute the matrix element
$$S_{fi}=<f|\...
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CPT invariance and Soft Theorems
I am reading the paper IR Dynamics and Entanglement Entropy, written by Toumbas and Tomaras and I have a question on using the CPT invariance of the QED $S$-matrix elements in order to derive the ...
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