Qft Definition and 956 Threads

I'm reading peskin QFT textbook. In page 196 eq. (6.58) it says $$F_2(q^2=0)=\frac{\alpha}{2\pi}\int ^1_0 dx dy dz \delta (x+y+z-1) \frac{2m^2z(1-z)}{m^2(1-z)^2}\\=\frac{\alpha}{\pi}\int ^1_0 dz\int ^{1-z}_0 dy \frac{z}{1-z}=\frac{\alpha}{2\pi}$$ I confirmed the conversion from the first line...

I am reading Tong's lecture notes and I found an example in which there are several aspects I do not understand. This example is aimed at: - Understanding what is the analogy in field theory to the fact that, in classical mechanics, rotational invariance gives rise to conservation of angular...

No-Nonsense Quantum Field Theory: A Student-Friendly Introduction by Schwichtenberg, Will let you know how it is when I read it. More details here

I want to know what are the QFT topics that I need to understand in order to proceed in reading papers on entanglement entropy such as, Entanglement Entropy and Quantum Field Theory Entanglement entropy in free quantum field theory Entanglement entropy: holography and renormalization group An...

Hello, I have been following Tong's notes on QFT and have found them to be a great introduction. I am almost at the end and am trying to figure out how to proceed. I have seen recommendations on David Skinner's notes, but I think I want to use a textbook either with Skinner's notes or maybe...

I don't understand a step in the derivation of the propagator of a scalar field as presented in page 291 of Peskin and Schroeder. How do we go from: $$-\frac{\delta}{\delta J(x_1)} \frac{\delta}{\delta J(x_2)} \text{exp}[-\frac{1}{2} \int d^4 x \; d^4 y \; J(x) D_F (x-y) J(y)]|_{J=0}$$ To...

This is from Horatio Nastase "Intro to Quantum Field Theory" book (Cambridge University Press, 2019) , chapter 59. The reader is supposed to massage equation (3) into equation (4) with the help of the given polylogarithm formulas (1) and (2). I do not see at all how that's possible...

Can someone please explain what the author does here in 15.59? I do not understand both steps. Neither the rewriting of the derivative, nor the integral. thank you

I got as far as: $$[\hat \phi(x), \hat \phi(y) ] = \int \frac{d^3p}{(2\pi)^{3}(2E_p)}(\exp(-ip.(x-y) - \exp(-ip.(y-x))$$ Then I simplified the problem by taking one of the four-vectors to be the origin: $$[\hat \phi(0), \hat \phi(y) ] = \int \frac{d^3p}{(2\pi)^{3}(2E_p)}(\exp(ip.y) -...

Hi everyone, My university has completely scrapped an undergrad Intro to QFT course and I am essentially left with no choice but to do self-study with no (worst-case scenario) external guidance. Are there notes or texts that can be used for such a purpose? Would be a nice bonus if there's a...

Trying to burnish some lost skills and pick up some new ones.

Hello, I have a simple question : are there, today, practical applications of qft (elsewhere than in particle physics) ? By applications, I mean, did we design stuff with the help of this theory ? Thanks !

I've been reading about Quantum Field Theory and what it says about subatomic particles. I've read that QFT regards particles as excited states of underlying quantum fields. If this is the case, how can particles be regarded as objective? It seems to me that this also removes some of the...

Li=1/2*∈ijkJjk, Ki=J0i,where J satisfy the Lorentz commutation relation. [Li,Lj]=i/4*∈iab∈jcd(gbcJad-gacJbd-gbdJac+gadJbc) How can I obtain [Li,Lj]=i∈ijkLk from it?

In all books about QFT I have seen I can not find anything about what a localized particle concept is. Suddenly I found this note in Zee's 'QFT in nutshell' page 4: "As usual, we can form wave packets by superposing eigenmodes. When we quantize the theory, these wave packets behave like...

I'm currently working out quantities that include the vector and axialvector currents ##j^\mu_B(x)=\bar{\psi}(x)\Gamma^\mu_{B,0}\psi(x)## where B stands for V (vector) or A (axialvector). The gamma in the middle is a product of gamma matrices and the psi's are dirac spinors. Therefore on the...

In an earlier question I asked if the EM field was truly a separate field from the matter field in QFT, as it's field structure is naturally complementary to phase changes in the matter field in just the right way to restore gauge invariance (poorly formed question, but hopefully you get the...

Hello everybody, In all QFT courses one starts very early with commutation and anti-commutation relation. My main question is why do we do this and what is the motivation? I have already asked few people including our professor but could not get a clear answer. I am talking about the...

At the beginning of every course in QFT we are told that, unlike in ordinary QM in which the position variable is a physical observable , the position variable in QFT is just a label. Yet there are areas within QFT where the position variable is treated like a real physical degree of freedom...

In QFT a photon with arbitrary energy can interact with an electron.But in QM and Solid State Physics, if energy of photon smaller than energy gap of electron then photon can not interact the electron.So it seems to me there is a contradiction?

A central feature of classical GR that it is background independent and operates via a curvature in space-time. As I understand it, this is not true of the other Standard Model forces which are consistent with special relativity and operate in Minkowski space, in which forces are transmitted via...

Hi folks, I'm trying to get a grasp on some of the basic concepts of QFT. Specifically, I'm trying to picture what are the actual fields of QFT and how they relate to wavefunctions. There are already many helpful posts about those concepts, here and in other places, but some points are fuzzy...

Sorry in advance if this question doesn't make sense. Anyway, I am reading a paper about quantum field theory and the Whitman Axioms (http://users.ox.ac.uk/~mert2060/GeomQuant/Wightman-Axioms.pdf), and it describes a field (Ψ) as Ψ:𝑀→𝑉⊗End(𝐷) where 𝑀 is a spacetime manifold, 𝑉 is a vector...

Summary: In QFT, if we add a gauge breaking term to the Lagrangian, do we still need to introduce Faddeev-Popov ghost particles? Ghosts seems to be introduced to maintain gauge invariance. But suppose we have eliminated the gauge invariance, from the start, by explicitly introducing a gauge...

I should first acknowledge 2 important points. I don't read papers on QFT, and therefore barely know how to spell it. And second, although I read many papers on entanglement (theory and experiment) I don't know if I have ever seen much reference to anything I might label QFT (that being...

I haven't been up to date on the state of the art of the field for quite some years now; the contemporaneity of my knowledge ends with the review by Rivasseau, 2000. A quick gander at the topic over at the n-Cat Lab shows that practically nothing has changed. Is anyone working in the field here...

I am currently studying the Massive Thirring Model (MTM) with the Lagrangian $$ \mathcal{L} = \imath {\bar{\Psi}} (\gamma^\mu {\partial}_\mu - m_0 )\Psi - \frac{1}{2}g: \left( \bar{\Psi} \gamma_\mu \Psi \right)\left( \bar{\Psi} \gamma^\mu \Psi \right): . $$ and Hamiltonian $$ \int \mathrm{d}x...

I have always learned that a Hermitian operator in non-relativistic QM can be treated as an "experimental apparatus" ie unitary transformation, measurement, etc. However this makes less sense to me in QFT. A second-quantised EM field for instance, has field operators associated with each...

Because massive gauge bosons have a finite half life, are they excluded from the (infinitely, asymptotically remote?) in and out states of QFT? Or, to put it another way, are they restricted to the internal legs of Feynman diagrams, i.e. to being virtual only? We can see W and Z tracks in...

I'm getting confused by the perturbation theory aspect of problem 2.2 in this book. We have to show that the energy eigenvalues are given by $$E_n = \left(n + \frac{1}{2}\right) \hbar \omega + \frac{3\lambda}{4} \left(\frac{\hbar}{m\omega}\right)^2 (2n^2 + 2n + 1)$$ For the Hamiltonian...

It was recommended that I start separate threads, as I have quite a number of questions on QM & QFT. I'm including all the relevant information/quotes in this thread just for the sake of reference, but there are fewer questions. It might seem like an excessive amount of information but it's all...

Apologies if there are already an abundance of threads on related questions. I have tried searching for threads on here and have read quite a few, as well as reading other sources. I've kind of reached a point where I need help to parse some of the information that I have been reading and to get...

I am currently reading Particle Physics by Palash Pal. In one place, the author shows the Feynman diagram for the electron-proton scattering: Then, he writes the Feynman amplitude for the process: $$i \mathcal{M} \ = \ \left[ \bar{u}(\vec{k'}) i e \gamma^\mu u(\vec{k}) \right]...

Following up on @A. Neumaier's excellent series of articles on virtual particles, I'm confused about one thing (well of of several). If you pop over to the discussion of virtual particles on Matt Strassler's page, he mentions that, for example, an excitation in the photon (em) field will also...

Let's for example consider the Z boson. It can't directly be detected; so is it ever really correct to draw it as an external line on a Feynman diagram? I've seen processes involving it before be written as something -> Z + something, then Z -> ... but since unstable particles aren't really on...

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A lecturer today told the class that relativistic QM for single particles is flawed by showing us that for a state centered at the origin, it was possible that ##Pr(\vec{x}>ct)>0##. He said that this was down to the fact that we should be considering multi-particle states in relativistic...

I have recently started a book on QFT: A First Book of QFT by Amitabha Lahiri and Palash B. Pal. It is very well written until the chapter of renormalization, where, before correcting the ultraviolet and infrared divergences, the book itself diverges, and I couldn't make meaning out of what they...

I've been struggling with a somewhat-recent paper by Charles Francis, "A construction of full QED using finite dimensional Hilbert space," available here: https://arxiv.org/pdf/gr-qc/0605127.pdf But also published in...

I am reading the A First Book of Quantum Field Theory. I have reached the chapter of renormalization, where the authors describe how the infinities of the self-energy diagrams can be corrected. They have also discussed later how the infrared and ultraviolet divergences are corrected. Just before...

While reading the electromagnetic vertex function at one loop, the authors of the book I am reading, wrote down the following vertex function: corresponding to this Feynman diagram: The superscript in ##\Gamma## is the number of loops being considered. My problem is with the equation. I...

So there is no a full quantum theory of gravitation. However, there are instances where quantum effects due to gravitation have been studied. Like Gravitational neutron interferometry https://arxiv.org/pdf/1701.00259.pdf or maybe gravitational decoherence...

I am studying a beginner's book on QFT. In a chapter on electromagnetic form factors, the authors have written, using normalized states, $$\begin{eqnarray} \langle \vec{p'}, s'| j_\mu (x) |\vec{p}, s \rangle \ = \ \exp(-i \ q \cdot x) \langle \vec{p'}, s'| j_\mu (0) |\vec{p}, s \rangle...

Full quantization of gravity is a big issue, but that's not what I'm asking here. I'm asking about quantum effects that involve any form of gravitation (Newtonian or GR) but that don't require a full quantization of GR or anything like that. Things like gravitational neutron interference or the...

How is the contact, or the interaction of electrons, if, according to Zeno's paradox, the distance between objects is divided into infinite points?

I am currently studying QFT from this book. I have progressed to the chapter of QED. In the course, the authors have been writing the Lagrangian for different fields as and when necessary. For example, the Lagrangian for the complex scalar field is $$\mathcal{L} \ = \ (\partial ^\mu...

In Bundell's QFT book, the second-quantised, pairwise interaction potential was defined as: in a later step, this was re-written in a momentum-space representation 1. I don't understand why it goes from ##V(x, y)## to ##V(x-y)##, why do we consider only this form of interaction potentials...

I am studying QFT from A First Book of QFT. It is a very well-written book. However, due to some personal reasons, I cannot buy the printed book at this moment. So I borrowed this book from a person (who, in turn, borrowed it from his university library), and scanned it. Everything is fine...

Hi, Let be a scalar field φ that permeates all space. The quantum of the field has a mass m. The field is at the minimum of its potential. When this minimum is for φ≠0 (a broken symmetry), the quantum may be observed by exciting the field, as with the Higgs boson. But if the symmetry is not...