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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 the Hermitian conjugate of a column vector still be column vector?

From what I understand, contravariant vectors are represented by column vectors, and covariant vectors are row vectors. So for a QED current, say $j ^ { \mu } = \overline { \psi } \gamma ^ { \mu } \...
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Magnetic field and magnetic forces and polarity

When the polarity of the voltage applied to a dc motor is reversed, the direction of motion does not reversed. Why not? How could the direction of motion be reversed?
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Magnetic field and magnetic forces

Hall-effect voltages are muchh larger for relatively poor conductors (such as germanium) than for good conductors (such as copper), for compatible currents, fields, and dimensions. Why?
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Dirac equation and Hamiltonian for a collection of magnetic monopoles

I am trying to understand a mathematical comment by Eugene Wigner in some old lecture$,^{[1]}$ "The Hamiltonian of the Dirac equation for two oppositely charged monopoles is not self-adjoint." What ...
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Frequency gap between neighbouring spectral lines

According to classical theory the atomic line spectra are discrete and their frequencies quantized. Have the newer quantum theories changed anything since then, giving some other expressions for the ...
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Magnetic forces in physics

Could an accelerator be built in which all forces on the particles, for steering and for increasing speed, are magnetic forces? Why or Why not?
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Magnetic force and field involving simple harmonic motion

Is there a simple harmonic motion when the electromagnetic compass was made by suspending a coil. The coil align itself perpendicular to the horizontal components of the earth's magnetic field and ...
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Can electromagnetic radiation affect the ability to navigate using magnetic field of Earth?

Recently I came several articles how Electromagnetic Radiation (EMR) is leading to a decline in the population of bees and birds. The important point being emphasised is that EMR affects their ...
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Bound system in QED

I am trying to read a paper on decays of Positronium. However, I am not able to see how to get equation 11. Could you please give some hints on how to derive it.
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What is the difference between QFT and QED? [closed]

What is the difference between QFT and QED? In QFT electron is field quanta, what is electron in QED?
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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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A thought experiment that can contradict “lack of an absolute reference frame” principle! [duplicate]

Although it seems similar to the other question: If a mass moves close to the speed of light, does it turn into a black hole? It is not the same. That question is about what happen to a mass with very ...
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51 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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136 views

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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Which papers are necessary to understand the Renormalization of Quantum Electrodynamics?

Ive been studying non-abelian gauge invariance, and headed towards studying renormalization of Yang-Mills theories. I figure it would he helpful to first understand the Abelian QED case. Which papers ...
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Stern-Gerlach experiment deflection

The deflection in Stern-Gerlach experiment is $z=\frac{F_{z}}{m}(\frac{d_{1}}{v_{y}})^2+\frac{F_{z}}{m}\frac{d_{1}}{v_{y}}\frac{d_{2}}{v_{y}}$, where $v_{y}$ is constant velocity of silver atom from ...
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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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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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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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Where does the “-”sign come from in formula (22) of Diracs principles of Quantum Mechanics, section 75?

When inserting (21) into the defining formula (20) of Delta, I don't see why there should be a minus sign. Formula (22) is used several times in section 75, so it should be correct; but I can`t see ...
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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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72 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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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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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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LSZ for scalar QED

Can someone direct me towards a reading where the Feynman rules for scalar QED are derived? I want a proper step by step derivation, not just the statement of the rules.
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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 ...