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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Simple questions on Introductory QED

I'd like to address three issues about QED: Regarding the quantization of the electromagnetic field: It can be achieved by means of adding an extra 'gauge-fixing' term in the Lagrangian: $\,\mathcal{...
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Quantization of free EM field, doubt about the field operators?

this is the first time that I study fields quantization and in particular I'm starting with the free em field. Previously I've just studied the non relativistic, Schrodinger equation for a non zero ...
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How to calculate 3 steps in Stern–Gerlach experiment? [closed]

How can we calculate Output3 and Output4, see picture If we defined vectors: up(T,p)=[cos(T/2)(cos(-p/2)+isin(-p/2)); sin(T/2)(cos(p/2)+isin(p/2))] um(T,p)=[-sin(T/2)(cos(-p/2)+isin(-p/2));cos(T/2)...
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Schrodinger equation for free EM field

The question come from the fact that I've seen for the first time in my life the quantization of a field, in particular of the free em field. I've study how it is possible to write the energy of the ...
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Why aren't there any soft corrections to the anomalous magnetic moment?

Why aren't bremmstrahlung effects considered in the computation of the anomalous magnetic moment? Surely they affect the cross-section and via the Rosenbluth formula ought to give "finite" corrections ...
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w do I draw the tree-level Feynman diagram if the interaction term only represents the scalar particles?

Consider the process $$e^+(p_1)+e^−(p_2) \to S(p_3)S^∗(p_4)\tag{1}$$ $S/S^*$ is scalar particle/antiparticle described by the complex scalar field $\phi$ coupled to QED through the Lagrangian: $$\...
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How can I simplify the amplitude of the following Feynman diagram as to obtain equation (v)?

I am trying to find the amplitude for the following pair production $$\gamma(p_1) + \gamma (p_2) \to e^- (p_3) + e^+ (p_4)\tag{1}$$ In an old exercise I am given the possible answers but I am not ...
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Regulators and Transversality (Wards identity)

In QED, why some regulators obey transversality (Ward identity) and some not?
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During particle-antiparticle annihilation, are the photons expelled perfectly perpendicular?

During particle-antiparticle annihilation, are the photons expelled perfectly perpendicular to the original direction of the particle-antiparticle pair? There is very little information on the web ...
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What is the probability of QED interactions?

In Feynman diagrams of QED vertices of interaction are often labelled by the amplitude sqrt(alpha) where alpha is the e.m. fine structure constant. When higher order diagrams are constructed, each ...
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Fundamental Limits for Photon Detection

In quantum electrodynamics "photons don't have positions". The physical relevance and consequences of this fact has been discussed on this site 1. (Further relevant questions about the concept of ...
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Question about gluons and the W-boson regarding Feynman diagrams

My questions are: 1) Does a gluon always have no charge? 2) Is the W-boson always positive or negatively charged? I thought these two statements were correct, but I came across an exercise that ...
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Question about Feynman diagrams

In the picture there are feynman diagrams for two reactions. My question is: Why aren't 6.3 and 6.4 possible for the first reaction? And as a sidenote, I don't really have a good source for the rules, ...
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Calculating traces for triangle diagrams with massless fermions

I am following Schwarz Quantum Field Theory textbook. In particular, I am looking at triangle diagrams with massless fermions. On pg. 623 - 624 Schwarz attempts to calculate $q_\mu^1 M_{5}^{\alpha\mu\...
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What happens to Coulomb's law at small distances? [closed]

I searched in the forum and found the maximum distance is $r=1.75\times 10^{-15} m$. Ok, imagine an electron hits a plate with charge of 1 proton, the result of Coulomb's law is $230$ Newtons. ...
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Axial anomaly at the level of particles

Consider pure QED with massless electrons. Due to the axial anomaly the axial current is not conserved: $$ \tag 1 \partial_{\mu}J^{\mu}_{5} \sim F_{\mu\nu}\tilde{F}^{\mu\nu} $$ On the other hand, it ...
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Expansion of trace in photon self-energy

I am studying through the photon self-energy $$ i\Pi_{\mu\nu}(q) = \int\frac{d^4 k}{(2\pi)^4}Tr\left[(-ie\gamma_\mu)\frac{i(\require{cancel}\cancel k+m)}{k^2-m^2+i\epsilon}(-ie\gamma_\nu)\frac{i(\...
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Coherent drive Hamiltonian

Sometimes in the light-matter interaction described by the Jaynes-Cummingsa model, an additional coherent drive is included which drives the light in the cavity. I've encountered this so many times in ...
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Linear Structure of Classical theory

I have been studying QFT from Timo Weigand’s lecture notes and in the chapter ‘Quantisation of spin-1 fields’, he describes the Feynman rules for QED and after some examples, there is subsection named ...
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Why does the photon have no antiparticle?

Considering the QED Lagrangian we get a solution of the form $A^{\mu}$. This solution has four degrees of freedom (dof). With the weak Lorenz gauge we reduce it to two dof. With this condition we also ...
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Perturbative expansion of the S-matrix in QFT

Beginner to QFT - While Taylor expanding the exponential term of the S-matrix, why is the 2nd order term (quadratic time integration term) written with two different dummy variables for time? (...
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Intuitive microscopic explanation of Lenz's Law?

Consider a horizontal wire loop through which a magnet is dropped. I understand the macroscopic explanation. The moving magnet generates an electric current in the wire loop(counterclockwise when ...
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Pauli Term contribution to muon' s anomalous magnetic moment

I'm trying to compute the contribution of a non-renormalizable term in the QED lagrangian to the muon's anomalous magnetic moment. The term in question is: $\frac{ie}{\Lambda}\bar{\psi}\sigma^{\mu\nu}\...
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Chiral anomaly for massless Dirac fermion

Let us assume we have a single flavor massless Dirac fermion with Lagrangian $\mathcal{L} = \bar{\psi}i\gamma^{\mu}D_{\mu}\psi + \mathcal{L}_{gauge}.~$ Due to chiral anomaly, chiral symmetry is not a ...
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Why do the modes of a string add up in the classical wave funcion but don't quantum mechanically?

When comparing a classical and a quantum string, the resulting wave function is made up of the sum of the individual modes for the former but the product for the latter. That is at least what I gather ...
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Electron dressing and photon probing

So I have just gone over a lecture on electron dressing whereby an electron dresses itself in a foam of electrons/positrons/photons through photon emission and absorption (see image). My lecturer ...
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What is the smallest virtual photon wavelength created from the repulsion of two charged particles (i.e two protons)?

Since the repulsion of two charged particles is mediated through virtual photons. What is the theoretical smallest wavelength these two particles create or is it a range of wavelengths. Is it around ...
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Vertex correction in QED

I've been working through the chapters in Schwartz on the renormalisation of QED, and I have some confusion to do with the form of the Vertex correction. By my understanding, the correlation function ...
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What does phonon exchange do in the theory of superconductivity?

In the theory of superconductivity, the phonon-mediated electron-electron scattering leads to an effective interaction, the BCS hamiltonian,$$\hat{H}_{\rm BCS}=\sum\limits_{\vec k,\sigma}\epsilon_{\...
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References on infraparticles in QED

I recently became interested in a notion of infraparticles as "true" scattering states in, for example, QED. It is well known that S-matrix elements in QED suffer from infrared divergences due to ...
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Kallen-Lehman and one particle state of electron for QED

We did the Kallen-Lehman procedure in lectures for phi to the fourth theory. We also defined the wavefunction renormalisation. At the end our lecturer briefly mentioned that to carry it over to QED ...
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Some questions about generalized symmetries

The topic of generalized symmetries is rather new, as far as I understand, the first paper on them was - https://arxiv.org/abs/1412.5148. And I would like to grasp a deeper understanding of them. ...
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Does external $B$-field affects cross-sections at colliders?

The answer is yes https://arxiv.org/abs/1901.04322 this is article related to QFT computations, but what is important here is that the cross-sections for various diagrams DO! depend on external ...
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Doubling the intensity of a quantum field plane wave

To doubling the intensity of a classical electromagnetic plane wave of a specific wave number we simply multiply it's amplitude (which is a number) by a $\sqrt 2$ factor. But for a quantum field ...
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Does the $U(1)$ vector current flip under charge conjugation?

The conserved $U(1)$ current of the Dirac Lagrangian is given by $j^\mu = \bar{\psi} \gamma^\mu \psi$, where $\bar{\psi} = \psi^\dagger \gamma^0$. As this is interpreted as electric current I would ...
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How do we know how many Feynman diagrams to draw for a particular order?

For the purposes of this question, I'll limit the question to quantum electrodynamics, although this question could just as well be asked of electroweak theory and QCD. For a particular order of ...
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free fermion- monopole operator in scalar $QED_3+$ Chern simons term equivalence proof?

In most papers discussing 3D Abelian bosonization duality, they say that monopole operator in scalar $QED_3+CS$ is dual to free fermions. How do they know it, because I have never seen an actual ...
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Electrons scattering vs. electrons scattering + photon

I looking for ratio of probabilities of 2 processes: $$ e^+ + e^- \to e^+ + e^- $$ $$ e^+ + e^- \to e^+ + e^- + \gamma $$ as function of photon energy and momentum. I think it is well-known ...
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Infrared divergences: total energy of soft photons

One way to deal with IR-divergences in QED is sum over soft photons, which can't be detected due to finite sensitivity of detector: only photons with energy bigger that resolution of detector $E>E_{...
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Resources for One-Loop Calculation in QED

I am recently trying to study the calculation on one-loop diagrams in QED. Since the most resources i found where rather cryptic since they where very very general i wanted to ask whether or not there ...
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Why are quantum mechanical observables time-independent?

I am aware of the two pictures, namely the Schrödinger and Heisenberg pictures, where the time dependence is carried by the state in the former and by the operator in the latter. However, why does it ...
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Question about cavity qed

I am confused about the notion of atomic dipole decay rate and atomic polarization decay rate. What is the difference between two notions?
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On the nature of (magnetic) force

Imagine a metal object attached to an electromagnet that would otherwise fall to Earth. Does the magnetic field do work in resisting the fall? If so what are the force carriers? Indeed what are the ...
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Recommendations of articles about the Feynman theory of positron

I am studying about positrons and I would like a recommendation of an article that explain the ideas of Richard Feynman about the interpretation of the solutions with negative energies of the Dirac ...
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Can an observable be invariant under local $U(1)$ but not under global $U(1)$?

Consider a quantum field theory with two fields, a complex scalar field $\phi$ and a $U(1)$ gauge field $A$. Both fields are dynamic fields, not background fields. Suppose that spacetime is ...
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Why does the chances of particular Feynman diagram occurring reduces by 1% at each photon-electron interaction?

I saw a youtube video regarding Quantum Electrodynamics which explained how one can eliminate the Feynman diagrams with complex photon-electron interactions or loops. The guy explained that each time ...
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Tensor structure of the one-loop vacuum polarization in scalar QED

I'm working on the book by Schwartz to study QFT. This question concerns the evaluation of the vacuum polarization loop in scalar QED. Some more details of the calculation may be found in Schwartz ...
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Photon mass Infrared divergence regulization in the one-loop electron self-energy in QED

So basically I'm trying to calculate the one-loop mass and field strength counterterms from the electron's self-energy in QED using Pauli-Villars regularization (i.e. some heavy particle of mass $\...
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Functional determinant in scalar QED

I'm trying to integrate out the scalars from the path integral in scalar QED, but I encountered an integral I don't know how to do. The model is $S = \int_{\mathbb{R}^4}d^4x \left( -\frac{(F_{\mu\nu})...
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Fine structure constant and the renormalisation group

I read "The fine structure constant, alpha (α), describes how electromagnetic radiation affects charged particles. It has the numerical value 0.007297351" Given it relates to the electric charge ...

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