Quantum field theory Definition and 559 Threads

On May 18th, I presented a Colloquium for the School of Engineering and Physical Sciences at North South University, Dhaka, Bangladesh, with the title "A Dataset & Signal Analysis Interpretation of Quantum Mechanics", by Zoom. I attach a PDF of the slides and the YouTube video is here. I am...

I'm currently going through Peskin and Schroeder's Intro to QFT textbook, chapter 4.2 "Perturbation Expansion of Correlation Functions". So we use the evolution of an operator in the Heisenberg picture from some time t0 to an arbitrary time t>t0 assuming we know how the field looks at t0. Then...

I had two rather long questions about the recent programe on searching for UV-completions of EFTs through positivity bounds (that is, UV completions that obey fundamental constraints given by QFTs: unitarity, locality, causality, analyticity and Lorentz invariance) Question #1: The EFT-hedron...

Greetings and salutations from the Swamp, aka Florida. For most of my life, I've been incredibly fascinated with the fields of Physics and Astrophysics. I've, also, been pretty lazy in regards to formal education. And that's a point of fact, not relative to an observer (lol). Lately, as I age...

I am self-studying QFT in the Schwartz book "Quantum Field Theory and the Standard Model", currently I am struggling to understand the all-orders proof that ##Z_1=Z_2## using Ward-Takahashi identity (page 352). He states that ## -ie_R\Gamma^\mu ##, which is the sum of the 1PI contributions to...

I'm trying to explicitly find a projective unitary scalar representation of the Galilean group. I'll denote a generic element of the group by ##(a, {\bf b},R, {\bf v})##, corresponding respectively to time translation, space translation, rotation and boosts. In a representation with central...

I've managed to account for all the terms except for two, which seem to have a minus sign I cannot get rid of. When expanding the variation, one of them comes from the ##\phi## variation: $$-i \partial^\mu \phi \epsilon^\dagger \sigma^2 \partial_\mu \chi^* =-i \partial^\mu \phi \partial_\mu...

Hi everyone! I’m a physicist at heart, drawn to big questions about the universe. My thesis journeyed through String Theory and the Maldacena conjecture a long time ago, but three years ago, I leapt into AI with a PhD focused on Reinforcement Learning. It turns out, physics and AI aren’t so...

I am a final year Mathematics and Computing undergraduate. I am expected to submit an extensive B.Sc. thesis in four months. I have previously studied multivariable calculus, differential forms, chains, and a little bit of Theory of manifolds (Calculus on Manifolds, Michael Spivak). I am...

I found some excellent videos from Berkeley on what QFT is. https://www.youtube.com/@hitoshimurayama2746 The view is that QFT is simply a multi-particle ordinary QM. The videos give the full details, so I won't say anything else except to mention some highlights. Particle creation, Compton...

Hello, I sometimes read that the entanglement of the vacuum state of a field -- maximal and ubiquitous -- is an inescapable axiom of QFT. In articles often oriented towards AQFT (like SJ Summers' one, Yet more ado about Nothing) but also in this intervention by Susskind (from 32mn30...

I'm trying to understand this paper (https://arxiv.org/abs/1709.02813) in which the authors try to build a wavefunction for the universe without assuming locality and unitarity, so they would be rather emergent from geometrical constructs called "polytopes" and not assumed from the start (they...

In Peskin and Schroeder's QFT book, while deriving the cross section formula for particles ##A## and ##B##, a Dirac delta appears in Eq 4.77: \begin{align} \nonumber \int d\bar{k}^z_A \, \left. \delta ( F ( \bar{k}^z_A ) ) \right\vert_{\bar{k}^\perp_A = k^\perp_A, \, \bar{k}^\perp_B = k^\perp_B}...

Dear group members, Can you express your opinion on the following recent (2023) articles insisting that single particles are split in parts in double slit and in Mach -Zehnder interferometer.Is this splitting compatible with QM/QFT? Parts of the abstracts are included here. The full articles...

I am trying to understand how would one opt to solve this open problem?, if there are some objects in the non-constructive-axiomatic QFT which mathematically are ill-defined. One such ill defined notion is of virtual particles. I tried to understand what constitutes a virtual particle. For...

According to a recent paper (https://arxiv.org/abs/2305.18521) (explained here: https://www.ru.nl/en/research/research-news/eventually-everything-will-evaporate-not-only-black-holes) every massive object in the universe will evaporate in a similar way into Black Holes through Hawking radiation...

There is a paper called "On nothing" (https://arxiv.org/abs/1111.0301) which goes on to argue that the universe could not have arisen from a state without spacetime (as some proposals do using quantum fluctuations to explain how the universe was born without spacetime) However, there is a...

I am reading Peskin-Schroeder's QFT text, and there on pg. 98 Equation (4.56) they derive the expression for the vacuum energy density (relative to the zero of energy set by ##H_0|0\rangle = 0##): $$ \frac{E_0}{\rm{Volume}} = \frac{i\,\sum\text{(all disconnected pieces)}}{(2\pi)^4\,\delta^4(0)}\...

When computing the projection of time-evoluted state ## |x_j> ## on ## |x_{j+1}> ## it uses the 'completeness' of momentum basis ## \int \frac{dp}{2\pi} |p><p| ##. Next it explicitly states the form of Hamiltonian ## \hat{H} = \frac{\hat{p}^2}{2m}+\hat{V}(\hat{x_j},t_j) ##. Thereafter i believe...

I know that cosmology usually deals with general relativity but what about QFT, is it modified depending on the cosmological model? Or is it not something that change with the model used.

The level may be higher that Intermediate but I use that in the hope that I'll be able to understand the answer. I moved it here as it didn't really belong in the other thread. Feel free to move it further. I admit I haven't yet read the paper in it's entirety but I hope you'll bear with me. I...

from the little i understand there are certain symmetries that are broken in quantum field theory, i also know that gauge symmetries must cancel in order to avoid inconsistencies in the theory. if gauge anomalies need to be cancelled does that mean they dont correspond to a physical...

Following the calculation done in section 5.3 of Schwartz's QFT and The Standard Model, the matrix element, M, should have two contributions M1 and M2. M1=ϵ1ϵ3+ϵ1ϵ4 M2=ϵ2ϵ3+ϵ2ϵ4 However when I do these calculations I get that M1 = M2 = 1, ##|M|^{2} = |M1|^{2} + |M2|^{2} = 1+1 = 2##, which does...

So I understand that when a pair of particle and antiparticle annihilate each other, the result which is usually a photon, conserves the total energy of the 2 particles. My question is what if the energy of the particles was in fact destroyed and then new energy was created which just so happens...

I'm probably just complicating things, but I'm a little bit stuck with this problem. I started with just plugging in the definitions for ##\bar{\Psi}_a^c## and ##\Psi_b^c##. So I get $$\bar{\Psi}_a^c\gamma^{\mu}\Psi_b^c=-\Psi_a^TC^{-1}\gamma^{\mu}C\bar{\Psi}_b^T$$. After this I used...

Let's say we want to calculate the two-point Green's function for a fermion to a given order for a two particle interaction of the form ##U(x,y)=U(y,x)##. For the first order calculation we have to do all contractions related to...

Hi everyone! I'm going through Peskin & Schroeder's Chapter 19 (Perturbation Theory Anomalies) and it seems to be that equation 19.74 in page 666 has a minus sign missing on the RHS. Namely, I think the correct equation should read \begin{align} (i\not\!\! D)^2 = -D^2 -...

Well, I started with the first equation of motion for the scalar field, but I'm really not sure if I'm doing it the right way. \begin{equation} \begin{split} \frac{\partial \mathcal{L}}{\partial \varphi} &= \frac{\partial}{\partial \varphi} [(\partial_\mu \varphi^* -...

what is the likelihood of a vacuum decay happening, like is it something that is really considered and taken seriously by scientists or is it just wild speculation that is not really taken seriously but makes for good headlines? Also if vacuum decay does happen what exactly would be the...

I'm talking about their two volume set titled "Gauge Theories in Particle Physics". Amazon links: Volume 1 Volume 2 From looking at the books, it seems that the level is higher compared to Griffiths or Thomson. But, how does it compare to textbooks like Peskin & Schroeder or Schwartz...

From Wikipedia, I know that it is the case in GR that conservation of energy and other conservation laws are relegated to being local only I thought this wasn't the case in quantum field theory.

In this derivation, a basis of one-particle states ##\langle x|=\langle \vec x,t|## is expressed with the field operator, $$\langle x|=\langle 0| \phi (\vec x, t)$$ "Then, a Schrodinger picture wavefunction is $$\psi (x)=\langle x| \psi \rangle$$ which satisfies $$i \partial _t \psi (x) = i...

My understanding is (was) that "virtual particles" is a computational concept used in perturbation calculations in QFT e.g. in Feynman diagrams. This understanding is in conflict with the following note in Quantum Field Theory for the Gifted Amateur by Tom Lancaster and Stephen J. Blundell: and...

Hello, I'm interested in how measurement, entanglement, bell test etc are handled in QFT. It seems most QFT texts are being quite light on details on the subject. There would be is a preparation step as the start followed by some interaction and a measurement at the end. Interaction is usually...

First time in PF, I am sorry if I did not choose the right category. I have been doing theory in condensed matter (mostly numerics) as a PhD but I never got to learn proper quantum field theory (QFT). Aside from a few introductory courses at university, I never learned what is a many-body...

Hi guys! I was wondering if there is any difference choosing between d = 4 -e or d = 4 - 2e. If so, what are the impacts ?

Using above formula, I could calculate the given commutator. $$ [\epsilon^{\mu\nu\rho\sigma} M_{\mu \nu}M_{\rho\sigma},M_{\alpha\beta}]=i\epsilon^{\mu\nu\rho\sigma}(M_{\mu \nu}[M_{\rho\sigma},M_{\alpha\beta}]+[M_{\rho\sigma},M_{\alpha\beta}]M_{\mu \nu}) $$ (because...

For many years now, the theorist Nima Arkani-Hamed has lent his prestige and energy to a research program that aims to transform our understanding of quantum field theory, by using symmetries in the sums of Feynman diagrams to uncover perspectives on the theory not based in ordinary space-time...

In answering another question, I came across a nice paper by Weinberg: https://www.arxiv-vanity.com/papers/hep-th/9702027/ One thing that struck me was the following comment: 'In its mature form, the idea of quantum field theory is that quantum fields are the basic ingredients of the...

I'm struggling to understand the relation between phi4 theory,non-linear sigma model and ferromagnets. I've read this in a paper(Phys.Rev.B14(1976)3110):'It is possible to describe the long-distance behavior of the Heisenberg ferromagnets in two different ways:the phi4 theory which corresponds...

I have a question about following statement about ghost fields in found here : It states that introducing some ghost field provides one way to remove the two unphysical degrees of freedom of four component vector potential ##A_{\mu}## usually used to describe the photon field, since physically...

I am planning on pursing a Phd in Theoretical physics or Mathematical Physics in the next several years. My main motivation is doing research when it comes to grand unified theory. What areas of research (within that umbrella, in a theoretical sense) should I start looking into that are at the...

Hi Have been trying to solve the below question for a while, wondered if anyone could help. Considering the action $$S=\int -\frac{1}{2}\sum^2_{n,m=1} (\partial^{\mu}\phi_{nm}\partial_{\mu}\phi_{mn}+m^2 \phi_{nm} \phi_{mn})dx$$ under the transformation $$\phi'=e^{\alpha}\phi e^{-\alpha}$$...

I am reading the Schwartz's Quantum field theory, p.269~p.272 ( 14.6 Fermionic path integral ) and some question arises. In section 14.6, Fermionic path integral, p.272, (14.100), he states that $$ \int d\bar{\theta}_1d\theta_1 \cdots d\bar{\theta}_n d\theta_n e^{-\bar{\theta}_i A_{ij}...

Hello there, recently I've been trying to demonstrate that, $$\textbf{W}^2 = -m^2\textbf{S}^2$$ in a rest frame, with ##W_{\mu}## defined as $$W_{\mu} = \dfrac{1}{2}\varepsilon_{\mu\alpha\beta\gamma}M^{\alpha\beta}p^{\gamma}$$ such that ##M^{\mu\nu}## is an operator of the form $$...

I'm learning about the RG equation and Callan-Symanzik equation. In ref.1 they claim to solve the RG equation via the method of characteristics for PDE. Here's a picture of the relevant part: First, the part I don't understand - the one underlined in red. What does "compatible" mean here...

Let ##\Gamma[\varphi] = \Gamma_0[\sqrt{Z}\varphi ] = \Gamma_0[\varphi_0]## be the generating functional for proper vertex functions for a massless ##\phi##-##4## theory. The ##0## subscripts refer to bare quantities, while the quantities without are renormalized. Then $$\tilde{\Gamma}^{(n)}(p_i...

I am reading the Lancaster & Blundell, Quantum field theory for gifted amateur, p.225 and stuck at understanding some derivations. We will calculate a generating functional for the free scalar field. The free Lagrangian is given by $$ \mathcal{L}_0 = \frac{1}{2}(\partial _\mu \phi)^2 -...

I have a pretty naive question about quantization of real Klein-Gordon (so scalar) field ##\hat{\phi}(x,t)##. The most conventional form (see eg in this one ; but there are myriad scripts) is given by ##\hat{\phi}(x,t)= \int d^3p \dfrac{1}{(2\pi)^3} N_p (a_p \cdot e^{i(\omega_pt - p \cdot...