Quantum field theory Definition and 587 Threads

This was my attempt at a solution and was wondering where did I go wrong: -\frac{\partial}{\partial p_\mu}\frac{1}{\not{p}}=-\frac{\partial}{\partial p_\mu}[\gamma^\nu p_\nu]^{-1}=\gamma^\nu\frac{\partial p_\nu}{\partial p_\mu}[\gamma^\sigma...

Hi. Are these two books complementary, or do they have too much in common? https://www.amazon.com/dp/1107034264/?tag=pfamazon01-20 www.amazon.com/Quantum-Field-Theory-Standard-Model/dp/1107034736/ My problem is that I still don't quite understand the difference between university courses in...

Attempt at a solution: $$ -\gamma^{\mu}\gamma^{\nu}D_{\mu} D_{\nu} - im\gamma^{\mu} D_{\mu} + im\gamma^{\nu}D_{\nu} - m^2 =$$ $$ -\gamma^{\mu}\gamma^{\nu}(\partial_{\mu} + ieA_{\mu})(\partial_{\nu}-m) - I am \gamma^{\mu}(\partial_{\mu}+ieA_{\mu})+im\gamma^{\nu}(\partial_{\nu}+ieA_{\nu}) - m^2...

In the Peskin & Schroeder textbook, the ##\beta## function for the Gross-Neveu model is discussed in problem 12.2. After computing it, I have tried checking my results with some solutions found online. My problem is that they all disagree among each other (something quite recurrent for this book...

Summary: Does the "problem of time in quantum mechanics" go for Lorentz-invariant quantum mechanical theories like QED? Everything I read about "the problem of time in quantum mechanics," i.e. absolute time in QM clashing with relativity's relative time coordinate and relativity of...

Introducing the spacetime spherical symmetric lattice, I use the following notifications in my program. i - index enumerating the nodes along t-coordinate, j - along the r-coordinate, k - along the theta-coordinate, l - along the phi-coordinate. N_t - the number of nodes along t-coordinate. N_r...

In https://en.wikipedia.org/wiki/Lamb_shift about the lamb shift, it's mentioned that the change in the electron's frequency due to QED effects (vacuum polarization and self-energy correction) is about 1 GHz, which would translate to an energy change of hf = 6.63E-25 J. This is 3E-7 times of the...

I have a major in Mathematics and Mathematical Physics and I'm finishing a masters in Physics (just finishing to write down the dissertation really). I have also already enrolled the PhD course so that I need now to pick an advisor and a theme before june. My main interest since the early days...

Suppose that the spacetime is discrete, with only certain positions being possible for any particle. In this case, the probability distributions of particles have nonzero values at the points on which the wavefunction is defined. Do we need randomness in the transitions of particles in such a...

I have read on Wikipedia (https://en.wikipedia.org/wiki/Compton_wavelength) that we cannot measure the position of a particle more precise than half of its Compton wavelength, since the photon we would need will be so energetic to produce electron-positron pairs. How does the creation of...

Quantum Electrodynamics (QED) has some observable effects such as the lamb shift, which is mainly caused by the vacuum polarization and the electron self-energy. These effects contribute to the "smearing" of the electron in an unpredictable manner, other than the uncertainty we already have...

I know that in some Bohmian papers (like https://arxiv.org/pdf/quant-ph/0303156.pdf), electron-positron pair creation and annihilation is modeled by different methods like stochastic jumps in the configuration space. My question is, is there any Bohmian approach to reproduce all of the...

That said, my approach was to determine the energies and 3-momenta at the center of momentum reference frame for each particle, with a fixed s, and check it corresponds to each one of the above, but I'm having some trouble proving that, for example, E_A=\frac{s+m^2_A-m^2_B}{2\sqrt{s}}. I've...

I'm having trouble understanding a specific line in my lecturers notes about the path integral approach to deriving the Klein Gordon propagator. I've attached the notes as an image to this post. In particular my main issue comes with (6.9). I can see that at some point he integrates over x to...

Hello everybody. The Lagrangian for a massive vector field is: $$\mathcal{L} = -\frac{1}{4}F_{\mu\nu}F^{\mu\nu} + \frac{m^2}{2}A_\mu A^\mu$$ The equation of motion is ##\partial_\mu F^{\mu\nu}+m^2A^\nu = 0## Expanding the EOM with the definition of ##F^{\mu\nu}## the Klein-Gordon equation for...

Hello everybody! I have a big question about the renormalization: I do not understand why the "renormalization condition" is to impose the tree level result. Now I will explain it better. Let's take, for example, the electron self energy. The tree-level contribution is the simple fermionic...

Hello everybody! I have a question regarding the first step of the quantistic proof of the Goldstone's theorem. Defining $$a(t) = \lim_{V \rightarrow +\infty} {\langle \Omega|[Q_v(\vec{x},t),A(\vec{y})]| \Omega \rangle}$$ where ##|\Omega\rangle## is the vacuum state of the Fock space, ##Q_v##...

I just saw this public lecture and I really enjoyed it (the lecture begins at about 18 minutes into the video). He is an engaging and rather funny speaker. At the end there is a Q&A in which he for instance goes into some of the misconceptions about quantum mechanics. David Kaplan is also one of...

Hi everyone! Sorry for the bad english! So, just a quick doubt... Does things collapse from a wave of probability into a quantum field or is the wave in the quantum field the probabilistic wave itself? An example to make it clearer: Suppose we have an atom, it enters an atom interferometer, it...

Here we consider a black hole formed by gravitational collapse classically. We also consider a scalar massless Klein-Gordon field propagating on this background. To quantize the field we expand it in appropriate modes. The three sets of modes required are: The incoming modes, appropriate for...

Let us consider QFT in Minkowski spacetime. Let ##\phi## be a Klein-Gordon field with mass ##m##. One way to construct the Hilbert space of this theory is to consider ##L^2(\Omega_m^+,d^3\mathbf{p}/p^0)## where ##\Omega_m^+## is the positive mass shell. This comes from the requirement that there...

Hi. I'd like to ask what are the differences between Particle Physics, Quantum Field Theory and the Standard Model. I see these names of physics courses but I want to confirm if I understand the difference. My understanding is that when students learn particle physics in their undergraduate...

I am working on a research project where I intend to describe what the Penrose process would like in a sonic black hole. I have found what a rotating (Kerr) black hole looks like in the sonic analog: https://arxiv.org/pdf/1802.08306.pdf I have also found that the analog of massless particles...

Let's say we have a Dirac field ##\Psi## and a scalar field ##\varphi## and we want to compute this correlation function $$<0|T \Psi _\alpha (x) \Psi _\beta (y) \varphi (z_1) \varphi (z_2)|0>$$ $$= \frac {1}{i} \frac{\delta}{\delta \overline{\eta}_\alpha(x)} i \frac{\delta}{\delta \eta_\beta(y)}...

This theorem is summarized here: https://en.wikipedia.org/wiki/Coleman%E2%80%93Mandula_theorem I sort of understand the mathematical content of the theorem, that But what I don't understand is, intuitively, what sort of possibilities are ruled out. I've heard it said that flavor conservation...

Hi all, I am interested in advancing my education in theoretical physics, specifically topics concerning quantum field theories and quantum gravity. However, I have a somewhat rocky background as an early undergrad and while my Master's degree was achieved with great success in the classroom...

Homework Statement We are given the Lagrangian density: $$ \mathcal{L}=\partial^\mu \phi ^* \partial_\mu \phi - m\phi^* \phi +\sum_{\alpha =1} ^2 ( \overline{\psi}^\alpha (i\gamma^\mu \partial_\mu -m)\psi^\alpha -g\overline{\psi}^\alpha\psi^\alpha \phi^* \phi) $$ , where ##\phi## is a complex...

Consider two arbitrary scalar multiplets ##\Phi## and ##\Psi## invariant under ##SU(2)\times U(1)##. When writing the potential for this model, in addition to the usual terms like ##\Phi^\dagger \Phi + (\Phi^\dagger \Phi)^2##, I often see in the literature, less usual terms like: $$\Phi^\dagger...

Hello everyone! I have a question regarding the causality in QFT. If I take into consideration a real scalar field and I calculate: $$[\phi(x),\phi(y)] = 0 \space \space \space \space \space \text{if (x-y)}^2 < 0$$ Thanks to this relation we state that causality in QFT is preserved: a...

What is the probability that an electron will be annihilated by a virtual electron-positron pair?

What different between QFT and QED? In QFT electron is field quanta, what is electron in QED?

I am looking for some resources describing the following content: A light with wavelength ##\lambda## is propagating in flat spacetime. The light redshifts as its wavelength gets larger and larger. In quantum field theory, this causes an infrared divergence of the field. What I want to know...

In my physics education, I shied away from heavily theoretical stuff like General Relativity. I took the required sequence in Quantum Mechanics but having never used it on the job, much of that knowledge has faded too. I started a course in Quantum Field Theory but dropped it. I had friends...

Homework Statement The exercise needs us to first show that ##P^2## (with ##P_\mu=i\partial_\mu##) is not a Casimir invariant of the Conformal group. From this, it wants us to deduce that only massless theories could be conformally invariant. Homework Equations The Attempt at a Solution I...

I am looking for good references / clarifications on the subject. First of all, my question is concerned only with mathematical formulation of something that sort of plays the role of the Feynman path integral of the "standard" QFT. It is not concerned with the physical or philosophical...

I studied the work of a nano generator in quantu mechanics. The generator uses the principle of triboelectrics. How does this work in quantum field theory? I think that the electron (wave packet in the field) is in the atom in a small volume because the nucleus inhibits the propagation of the...

http://www.counterbalance.org/cq-turok/etern-body.html https://ned.ipac.caltech.edu/level5/Kolb/Kolb3_1.html) http://www.astronomy.ohio-state.edu/~dhw/A873/notes7.pdf) According to QFT, if you make repeated measurements of some property of the field then you will in general measure a...

I always had a tough time understanding how QFT relates to reality. Are these quantum fields (electron field, ect) physically real? Are they things that exist in space or are they just mathematical abstractions that help use calculate things?

I have taken one first QFT course last year which used Matthew Schwartz "Quantum Field Theory and the Standard Model" book. The course went all the way to renormalization of QED, although path integrals weren't discussed. Now I want to continue learning QFT and also I want to make a second...

This is a topic I've mentioned a few times before. Essentially the structure of matter in quantum gauge field theories is unclear to me. I have no clear question here, just some initial discussion points. So at the first level, it seems a particle based view of quantum field theory is difficult...

I am trying to compute the cross-section for the diagram below with a divergent triangle loop: where ##X^0## and ##X^-## are some fermions with zero and negative charge respectively. I am interested in low energy limits, so you can consider W-propagator as ##\frac {i\eta_{\mu\nu}} {M_w^2}##...

Hi , I need to enrich my knowledge in quantum field theory, please refer me to reference books in this branch. Thank's.

I was recently reading about annihilation and creation operators in particle physics using the model of an harmonic oscillator, and then quantizing it. This is fine. I can understand it. But how does this quantization of the energy of the harmonic oscillator manifest physically? Is it that only...

Hello! I am studying Zeidler's QFT Volume II, and I have a query on page 808: It is claimed that S Ψ^+_{p,s} = (sk)Ψ^+_{p,s} when p=p^3 k. I tried my hand at deriving this, but when we write S=S^1i+S^2j+S^3k, then the S^3k term acting on Ψ^+_{p,s} does give skΨ^+_{p,s}, but I don't see...

Consider a three dimensional representation of ##U(1)\times SU(2)## with zero hypercharge ##Y=0##: $$ L= \begin{pmatrix} L^+ \\ L^0 \\ L^- \end{pmatrix} $$ Then the mass term is given by [1]: $$ \mathcal{L} \supset -\frac m 2 \left( 2 L^+ L^- +L^0 L^0 \right) $$ I am wondering where the...

The logic of the Feynman Propagator is confusing to me. Written in integral form as it is below $$\Delta _ { F } ( x - y ) = \int \frac { d ^ { 4 } p } { ( 2 \pi ) ^ { 4 } } \frac { i } { p ^ { 2 } - m ^ { 2 } } e ^ { - i p \cdot ( x - y ) },$$ there are poles on the real axis. I have seen...

Homework Statement For massless particles, we can take as reference the vector ##p^{\mu}_R=(1,0,0,1)## and note that any vector ##p## can be written as ##p^{\mu}=L(p)^{\mu}_{\nu}p^{\nu}_R##, where ##L(p)## is the Lorentz transform of the form $$L(p)=exp(i\phi J^{(21)})exp(i\theta...

I start by outlining the little I know about the basics of quantum field theory. The simplest relativistic field theory is described by the Klein-Gordon equation of motion for a scalar field ##\large \phi(\vec{x},t)##: $$\large \frac{\partial^2\phi}{\partial t^2}-\nabla^2\phi+m^2\phi=0.$$ We...

After some reading, I'm quite confused about the vacuum state in interacting QFT. I've read the @A. Neumaier post on "The Vacuum Fluctuation Myth," where he notes that "bare quantum field theory with a cutoff, the vacuum is a complicated multiparticle state depending on the cutoff – though in a...

I think this could be an interesting discussion (unless I'm just totally off base): I don’t think were looking at things right in the atomic world. We represent everything as this wave particle duality which is not incorrect but is a great way to visualize particles and forces and their...