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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What is inside of Electron ¨Color Boxes?¨

What is inside the Electron Color Boxes. All the articles I read said that it was ¨Complicated Stuff¨ and all the videos just said what the outcome is but not what the color box is actually made of ...
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84 views

The $×$ in a QFT text is cross product? I 'dont think so

My friend said that the $×$ that appears in quantum field theory is a vector product but it makes no sense several times I solved the rules of Feynman and never had a vector product for me it is ...
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What is the expected energy density of the vacuum for QED Planck cutoff?

I would like to know the value of the expected energy density of vacuum in QED with Planck's energy cutoff in the units of kg/m^3 (mass density). I only find rough estimations in erg/cm^3 or joules ...
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67 views

1-loop correction to fermion propagator in Landau gauge

I want to calculate the 1-loop correction to the fermion propagator. I have already done the calculation in the Feynman gauge (done in Peskin & Schroeder for example) where the photon propagator ...
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$S$-matrix computation for QED [closed]

While expanding the s matrix term for qed, we get zero contraction term for the second order term of S matrix as shown. Then how to draw Feynman diagram for the zero contraction term?
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54 views

$q^2=4m^2$ as the threshold for creation of a real electron-positron pair

On page 252, Peskin & Schroeder remark that the branch cut of the quantity $$\widehat \Pi_2(q^2) \equiv \Pi_2(q^2)-\Pi_2(0) = -\frac{2\alpha}{\pi}\int_0^1dx\,x(1-x)\log\left(\frac{m^2}{m^2-x(1-x)q^...
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What part of the electron mass is due to Yukawa coupling?

Sorry if this question is wrong - then please correct it. A particle mass can be due to a Dirac mass term or due to a Yukawa mass term. In the standard model, which percentage of the electron mass is ...
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Classical point-charge self-energy in terms of momentum cut-off of QED

When computing the one-loop correction $\Sigma_2$ of the electron self-energy, Peskin & Schroeder on page 218 use Pauli-Villars regularization on a certain divergent momentum integral by making ...
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How can you imagine a photon?

Is it correct to imagine a photon as a superposition of states <photon + virtual electron-positron pair + virtual quark + antiquark + ...> pair? And the lower the photon energy, the lower the ...
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Is $[E_i(x), B_j(y)]=i \hbar \varepsilon_{ijk}\partial_k \delta^3(x-y) $ ? (and how to derive it?)

In a comment, user @Andrew says that $$[E_i(x), B_j(y)]=i \hbar \varepsilon_{ijk}\partial_k \delta^3(x-y). $$ Is this the case? Considering one of Maxwell's equations can be written: $$\nabla \times \...
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Deriving a general gauge-invariant photon propagator

My understanding is that for a $U(1)$ gauge field $A_\mu$, the most general gauge-invariant kinetic term in the Lagrangian that can be written down which satisfies gauge invariance is something of the ...
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What does bring us to the quantization of the fermion wave functions?

In the case of Electromagnetic fields, Einstein's observations about cavity radiation show the particle-like behavior of the EM fields inside a cavity(as we know Einstein showed the microstates of the ...
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Background field method for QED

I want to evaluate the 1-loop beta function for massless QED using background field method. This is my trying. First we separate the gauge field into $$A_\mu(x)=\bar{A}_\mu(x)+\delta A_\mu(x)$$ \begin{...
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What happens when a linearly polarised light is incident obliquely on a surface?

I want to know what happens when linearly polarised light is made incident at an oblique angle. In what way the linearly polarised light changes upon reflection.
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Photon Path Integral and Lorenz Gauge

I am reading Srednicki's QFT book (http://web.physics.ucsb.edu/~mark/qft.html). In chapter 57, specifically in page 343, the book stated that there's a problem with the path integral because the ...
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55 views

Source of hierarchy problem for fermions and bosons

In the beginning of a SUSY course, we computed $1$-loop level corrections to the mass of a bosons $\phi$ and a fermion $\psi$ in the theory \begin{align} \mathcal{L} &= \bar{\psi}(i\gamma^\mu D_\...
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49 views

How to deal with cross-terms in squared slashed covariant derivative in QED?

I am trying to compute the square of the slashed covariant derivative (the sum of the partial derivative and vector potential contracted with the gamma matrices) in terms of the square of the standard ...
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Non-linear QED gauge fixing, writing the effective Lagrangian

I have several questions about this problem. I have been given a non-linear gauge condition for a QED theory: $$F = \partial_{\mu}A^{\mu} + \frac{\lambda}{2}A_{\mu}A^{\mu}.$$ Then I need to write the ...
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49 views

What happens to an electron when it radiates a photon?

I recently came across this Feynman diagram: For a more simplistic diagram, I suppose even this would be adequate: As you can see in these diagrams, they radiate these virtual photons. The virtual ...
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About the validity of the dilute gas approximation

In the compact QED (cQED) in $(2 + 1)$ dimensions confinement /deconfinement property is described in terms of boundness of monopole-antimonopole pairs (Berezinskii-Kosterlitz-Thouless phase ...
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43 views

Polarization vectors with inverted momentum

Given a $2\rightarrow2$ body scattering problem in CM frame, i.e., $\gamma_1\gamma_2\rightarrow\gamma_3\gamma_4$ process, and the coordinate is chosen such that $\gamma_1$ is moving along $+z$-axis, ...
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Are gravitation and the Fine-structure constant related? [closed]

This NewAtlas article Evidence of "modified gravity" in 150 galaxies strengthens dark matter alternative discusses possible anomalies to gravity. The Fine-structure constant is likely to be ...
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Does light always take the shortest path?

Does light always take the shortest path? And is it possible to change the probability of a photon travelling to a point by only disturbing the paths that are far away from the shortest path?
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What is the physical meaning of the operators of the positive and negative frequency components?

In quantum optics, after performing the quantization of the radiation field, the field operator $E$ is often split into the positive- and negative-frequency parts as $$ E(\mathbf{r},t) = E^{\left(+\...
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41 views

How to obtain Heisenberg equation for expectation value of operator product given Heisenberg equation of each operator?

The problem is following: I have given two equations for creation and annihilation operators: $\dot{a}(t) = \left(-i\omega -\frac{\Gamma}{2}\right)a(t) \tag{1} $ $\dot{a}^\dagger(t) = \left(i\omega -\...
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Feynman loop diagrams physical meaning

I'm relatively new to Feynman diagrams and have a question about loops. Consider the following diagram: I understand the electron positron annihilation resulting in a photon but I do not understand ...
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77 views

Eletromagnetic waves & photons

I was thinking about how to reconcile the picture of the eletromagnetic wave as a changing electromagnetic field and as a collection of photons. If i have a charged particle, that is free in space and ...
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61 views

Spin of photons and angular momentum of classical radiation field. Are they connected?

Photons, the quanta of the radiation field, carry spin $-$ an intrinsic angular momentum. Classical radiation also has angular momentum having the expression $$\vec{J}=\frac{1}{\mu_0c^2}\int dV \left(\...
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How is the Coulomb potential infinity resolved in quantum field theory?

People always says that the infinity of the coulomb potential $V(r)=\frac{k}{r}$ as $r$ approach to zero is resolved in quantum field theory. I would like to know how this is done.
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36 views

Can you quantize a field of charge density?

If I wanted to develop a model of quantum electrodynamics, but instead of an electron field, I quantized the scalar charge density field that is used in Maxwell's Equations, would it be possible? If ...
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47 views

What does the inter-photon force look like (as mediated by electrons)?

Most often we think of photons mediating a force between charged particles (e.g. electrons and positrons), and it's a standard exercise in QFT to do the computation and find that, to leading order in $...
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Is Compton Scattering the “Abelian limit” of $qg \rightarrow qg$?

I have calculated the average over initial and sum over final states of the squared amplitude for both Compton scattering $e^-\gamma \rightarrow e^-\gamma$ (QED) and quark-gluon scattering $qg \...
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Time reversal and charge conjugation for scalar electrodynamics

What happens to positive electric charge when the time direction is reversed? my intuition is this will not effect the type of electric charge (positive or negative) but how can I show it rigorously ...
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1answer
81 views

Higher-Order Feynman Diagrams for $e^{+}e^{-} \rightarrow \mu^{+}\mu^{-}$

In his book "Modern Particle Physics" Mark Thomson has the following Figures for $e^{+}e^{-}\rightarrow \mu^{+}\mu^{-}$: (i) Concerning the first Feynman diagram in Figure 6.2: Couldn't the ...
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Physicists adding 3 decimals to the fine structure constant is a big accomplishment. Why?

Yesterday, a team of physicists from France announced a breakthrough in nailing down a "magic number" by adding three decimals to the the fine-structure constant (news article; technical ...
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Electron scattering from Coulomb potential in canonical formalism

I am trying to follow Zee's computation of the amplitude for the pictured process. I have already done it using the Feynman rules for writing amplitudes and now I am confirming the result in the ...
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1answer
50 views

Amplitude for electron scattering off structureless stationary nucleon

In Zee's QFT book, Section II.6, he gives the amplitude for this pictured process of an electron scattering from a structureless nucleon as $$ \mathcal{M}(P,P_N) = \cfrac{-ie^2}{k^2-m_\gamma^2} \,\...
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Fourier Transform of Coulomb potential in QFT

I am master student of particle physics and I want to find coulomb potential $V(r)$ from $\tilde{V}(p)$ in Schwartz-Quantum Field Theory and the Standard Model what I have as $\tilde{V}(p)$ from 16....
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487 views

Are quantum fluctuations observable?

I know I am asking out of my limits, but i felt relaxed thinking about this. Now I read somewhere about quantum fluctuations (that energy can be generated in randomly at two positions where total sum ...
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115 views

Functional derivative in Faddeev Popov method (Lorenz Gauge)

When applying Faddeev and Popov method (am using Peskin and Schroeder as reference), we use the identity: $$1=\int \mathcal{D}\alpha(x)\delta(G(A^\alpha)) \det\left(\frac{\delta G(A^\alpha)}{\delta\...
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Quantum Field Theory, questions about fields and their vacuum state [closed]

Are the fields in their empty state a single indivisible and static entity? I would also like to know if the gravitational field also has a vacuum state and if the other fields are permanently linked ...
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What is the relationship between the classical wavelength of light and the quantum mechanical wavefunction of a photon?

It is common to speak of the 'wavelength' of light. For instance visible light has a wavelength of around 400 to 700 nm. A single photon can also have a wavelength, given apparently by $\lambda = \...
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Deduction of Hamiltonian using Fourier coeficients on a vector potential $\vec{A}$

Given the operator $\vec{A}=\frac{1}{\sqrt{V}} \sum_{\vec{k}, \alpha} \varepsilon^{\alpha}\left(c_{\vec{k}, \alpha}(t) e^{i\left(\vec{k} \cdot \vec{r}-\omega_{k} t\right)}+c_{\vec{k}, \alpha}^{*}(t) e^...
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Derivation of interaction potentials of fundamental forces

In Gauge theory of weak interactions by Greiner and Müller, they show the following superb comparison of the interaction potentials between particles as a function of separation: I have never seen ...
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36 views

Feynman diagram

I am having trouble understanding how the Feynman diagram represents the dielectric medium and its interference on the screen of the charge of the electron. The diagrams are as follow: Could you ...
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Why is the $t$-channel diagram for Bhabha scattering allowed?

I thought that the individual lepton numbers $L_e$, $L_{\mu}$ and $L_{\tau}$ are individually conserved for each vertex. At least this is how I explained to myself that this Feynman diagram, ...
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Finding all Feynman diagrams of a physical process [closed]

I want to find all the contributing Feynman diagrams for the QED process $e^+ e^- \to \gamma\gamma$ up to fourth order in $e$. How can I go about solving this problem? And when I do solve it, how do I ...
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77 views

How to apply QED Feynman rules here?

I am reading Schwartz' QFT book, where in chapter 20, he discusses IR divergences. At the beginning of chapter 20.1.2, he considers the sum of the following diagrams in Feynman gauge and in the limit ...
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68 views

Do quantum fields interact in a vacuum state?

Interacting quantum fields (for example, electromagnetic and electron-positron) in a vacuum state (without real particles) continue to interact, or become free?
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Interaction of a photon with an electron-positron field

Although I am not very familiar with QED, I remember that the equations describing the photon propagator include variables related to the interaction of a photon with an electron-positron field. Our ...

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