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 does “Real-time” mean?

In the context of describing Real-time dynamics of Lattice gauge theories, have they specifically mentioned real-time in order to differentiate it from imaginary-time. Or does it have any other ...
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What, explicitly, happens as EM radiation travels from A to B?

I'm in my fourth year of a Masters Physics course, and am quite concerned that I don't fully understand this. Suppose a photon is emitted at point A and absorbed at point B one light-minute away. We '...
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Relation between radio waves and photons generated by a classical current

Several questions have been posted on Physics SE regarding the relationship between photons and electromagnetic waves, and several good answers have been given. Some of those questions are listed ...
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56 views

Can electron be polarized?

I know that electrons split into two beams when passed through a non-homogeneous magnetic field. But is electron polarized when passed through some substance? For example, light the polarization can ...
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Does a photon require an EM field to exist?

An excitation in the electromagnetic field is called an electromagnetic wave. The smallest possible part of the electromagnetic wave is called a photon. But if the photon is always accompanied by an ...
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340 views

Electromagnetic stress tensor is only traceless in 4D?

The electromagnetic stress tensor $F_{\mu \nu}$ is as we all know traceless in 4 dimensions. With $F_{\mu \nu} = \partial_\mu A_\nu - \partial_\nu A_\mu$ and $A = (A_0,A_1,A_2,A_3)= (\phi, A_1, A_2, ...
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Conserved current in scalar QED

Consider a theory of a free massless complex scalar $\phi$ which undergoes global $U(1)$ transformations. The conserved current associated to this symmetry is the usual scalar current $$ J^\mu = i\...
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Why does the fine-structure constant $α$ have the value it does?

This is a follow-up to this great answer. All of the other related questions have answers explaining how units come into play when measuring "universal" constants, like the value of the speed of ...
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164 views

How many counterterms does QED have?

I have read the statement that QED has four counterterms to cancel divergences. However, I have learnt that there are only three counterterms (vertex, electron propagator, photon propagator), which is ...
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In QFT people exchange electrons during touching? [closed]

Does in QFT static electricity work classically or is there a more fundamental explanation?
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126 views

Is the beam splitter transformation related to Hamiltonian?

Consider a general beam splitter with input 'ports,' 1 and 2. It mathematically described by a unitary transformation $\hat{U} = exp[i\theta(\hat{a}_1^\dagger \hat{a}_2+\hat{a}_2^\dagger \hat{a}_1)]$. ...
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Commutation relation in quantized electromagnetic field theory

I have a question regarding a proposed problem (Problem 4.8) in Rodney Loudon's book "The Quantum Theory of Light". Let $U(t)$ be an operator defined by $$ U(t)=\exp\left\lbrace\frac{i}{\hbar}\int\...
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What is the fundamental explanation for the existence of Electrostatic force?

To explain my question in a better way I will first talk about gravitation! Gravity is not a force and the effects of gravity are ascribed to spacetime curvature My comments: Gravity was explained ...
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Commutators in Gupta-Bleuler formalism for quantization of the electromagnetic field

In the Gupta-Bleuler formalism we have for the canonical momenta $$\pi_\mu=F_{\mu0}-g_{\mu0}\partial_\alpha A^\alpha. $$ Every resource I find online say that the equal time canonical commutation ...
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Electron interaction term in a external field

In quantum electrodynamics an electron $e_0$ interaction with an external field is given by term $\mathcal{L}_{\text{int}}\sim \bar{\psi}\gamma^\mu A_{\mu}^{c}\psi$ Where $A_{\mu}^{c}$ is ...
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Integrating over proton final momentum states

In Walter Greiner book QED, to derive the Born second the order approximation from electron proton scattering in the static limit of two photon exchange, he impose the following Condition in the ...
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How does the Schrödinger model of the hydrogen atom take into account radiation friction?

When one first encounters quantum mechanics, he learns about Bohr's model of the hydrogen atom and one of his biggest problems - electrons were accelerating and not emitting EM radiation (which is ...
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How can I prove the annihilation electron positron can't generate positron + muon? [closed]

How can I prove the process $e^{+}+e^{-}\rightarrow e^{+}+\mu ^{-}$ doesn't happen?
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Background fields in canonical formalism

In quantum electrodynamics problems involving background fields, most text books usually makes the following substitution $$A^\mu \rightarrow A^{'\mu}= A_0^{\mu}+A_{c}^{\mu}$$ Where $A_{c}$ is ...
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Orientation of momentum of a virtual photon

Picture a wire with current directed out of the page. The electrons in the wire emit virtual photons in all directions which mediate the produced magnetic field. What is the orientation of the ...
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82 views

Displacement current quantum mechanical interpretation?

while there are quite many classical explanations of displacement current to make Maxwell's equations work, see e.g. here: Displacement current - how to think of it , it sounds just a little bit like ...
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External radiation in quantum particle systems

In describing system of quantum particles external radiation is often assumed to be classical. Is there any text book that give a proof why can we assume that?
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Can a charged particle interact with its its own electromagnetic field? [duplicate]

Say an electron begin moving with velocity V back and forth very quick or at the speed of light, could it interact with its own previous pre existing electromagnetic field?
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The meaning of gauge-fixing in covariant quantization of the electromagnetic field

I am having trouble wrapping my head around the idea behind the covariant quantization for the electromagnetic field that is usually done in textbooks (I'm currently following Mandl & Shaw and ...
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150 views

Can the mass term be responsible for creation and destruction of particles?

In an interacting quantum field theory, for example, QED, the Dirac mass $m\bar{\psi}\psi$ is a piece of the free Dirac Lagrangian. On the other hand, the interaction term $j^\mu A_\mu=e\bar{\psi}\...
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Why does pair production produce an electron and positron with opposite spin?

So I was trying to understand quantum entanglement and the example that was used to describe an entangled pair of particles was of an electron and positron after it is formed from a photon in pair ...
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Does a source term for electric charge necessarily break global $U(1)$ symmetry?

The conservation of electric charge in, e.g., quantum electrodynamics $$\mathcal{L} = -\frac{1}{4}F^2 - A \cdot J + \mathcal{L}_\mathrm{matter}(J)$$ can be derived using the invariance under global $U(...
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Fock states and beam splitters

A classical beam splitter divides incoming light into two parts according to the reflection and transmission coefficients. A quantum beam splitter on the other hand, can be modelled using Fock states,...
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Feynman rule for trace over fermion loop

Where does the Feynman rule for "taking the trace over the matrix product arising from a fermion loop" come from? I can not derive it in the "usual way", that is writing the correlator all the way ...
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320 views

Diagrams involved in 1-loop electron self-energy in QED

I'm following the derivation of electron self-energy at 1-loop in QED on Peskin-Schroeder, page 216. To second order in the coupling the considered diagram (7.15) is The 2-point correlator at second ...
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Is it possible to derive the correct QED Lagrangian without demanding local gauge invariance?

Usually, the correct interaction term $A_\mu \bar{\Psi} \gamma_\mu \Psi$ in the Lagrangian is derived by demanding local gauge invariance. Is there any other argument that fixes the form of the ...
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In charge renormalization equation, $e=e_{0}^{2}\left[1-e_{0}^{2}A\right]$, how can an infinite $e_{0}$ and $A$ give finite $e$ in any limit?

In Griffiths elementary particle book (chapter 7, 'Quantum electrodynamics', equation 7.188), one gets the following equation for the vacuum polarization calculated to one loop correction. $$\frac{e_{...
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Why is the energy of $2s_{1/2}$ greater than the energy of $2p_{1/2}$ after the Lamb shift is taken into account?

The Wikepedia article here defines Lamb shift as a difference in energy between two energy levels $2s_{1/2}$ and $2p_{1/2}$ (in term symbol notation) of the hydrogen atom which was not predicted by ...
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The antiparticle of photon is itself

I'm not sure whether this question is redundant, but I think it is probably not due to the focus of the question. We might say that photon does have antiparticle and it is photon it self. I know for ...
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Interaction of charges [duplicate]

As it is known in Physics, two point-size charges (say two electrons) interact with each other through em forces. How this is happening? do they exchange photons? And if so, then do they exchange ...
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Does Electromagnetic Inertia has any relation with the emission of Electromagnetic Waves from Accelerated Charged Particles?

We know that Electromagnetic Fields have certain inertia in them. Lenz's Law is a good example to demonstrate Electromagnetic Inertia. Nature resists the change in the state of Electromagnetic Fields ...
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If electrons are waves, how do they repel each other? [closed]

Louis de Broglie said that electrons are waves. But how they repel each other?
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Why do the Electric and Magnetic Fields have Different Units?

I just finished my first upper-division E&M course and have a question. Why do the electric field and the magnetic field have different units if they are essentially rotations of each other? ...
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QED vertex correction, proper vertex function and meaning

I might be making great confusion in trying to interpret proper vertex function. I'm studying QED vertex correction. I'm just going to write down the pieces of the puzzle. So I know that the ...
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Diagrams Contributing to Electric Charge Correction (M. Schwartz)

In M. Schwartz's Quantum Field Theory and the Standard Model, he talks about the correction to the $g$-factor in Chapter 17. In Section 17.2 (Pg. 318), he is evaluating the diagram that gives the ...
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How much electrons can absorb a single photon?

In the one hand, energy can be emitted\absorbed only by a discrete portions. In the other hand - according to Coulomb law the higher distance - the lower force, because count of force lines per area ...
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Collapse operators in multi-level atomic systems?

I'm trying to understand the case of multiple ground states and excited states. Due to selection rules, usually we say there should be 3 collapse operators, namely C_+1, C_-1, C_pi, corresponding to ...
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Why are there no loop corrections to the photon mass? [duplicate]

I know that a question about why the photon is massless already exists, however it did not answer this question. First off, I do understand why the photon does neither have a bare mass term due to ...
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Is the magnetic field energy around a current carrying wire is similar to the electric field energy associated with an isolated charge?

What I mean by this question is, as we say that the electric field energy around a charge is the self energy of the charge, similarly can we say that the magnetic field energy around a current ...
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Is the electron field of QED similar to the Higg's field?

If I understand it (I probably don't...) the Higg's field is a field that permeates the universe, and its excitations are the Higg's bosons. It seems that this implies that the Higg's field is a ...
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Vector Spherical Harmonics and total angular momentum

In their book Akhiezer et al. give a definition of vector spherical harmonics (p.18 of Russian Edition) as $$\pmb{Y}_{j\ell m}(\pmb \Omega) = \sum_{m' \lambda} \langle \ell m' 1\lambda| jm \rangle Y_{...
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Wave energy in terms of classical and quantum mechanics [duplicate]

If there are two light waves of same amplitude but of different frequencies then their energy will be same or different? If same then how will you define the light waves as photons and will there be a ...
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Double photon emission, half photon absorption

Is it possible for atom with two electons to absorb one photon in this manner, $$|gg\rangle|n\rangle \to |ee\rangle|n-1\rangle$$ or for one electron to emit two photons like this $$|e\rangle|n\...
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What is interaction cross section of a photon and how to find it?

I encountered this term while reading about photon interaction with metal electrons. Is this equal to the scattering cross section or is it different? How to find it mathematically?
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What is the difference between photons in the E-Field and the H-Field?

It is well established that the photon is the propagator for the electromagnetic force. How are the set of photons used in the H-field behaving differently than those in the E-field? Is it different ...