What is Quantum field theory: Definition + 580 Threads
In theoretical physics, quantum field theory (QFT) is a theoretical framework that combines classical field theory, special relativity and quantum mechanics. QFT is used in particle physics to construct physical models of subatomic particles and in condensed matter physics to construct models of quasiparticles.
QFT treats particles as excited states (also called quanta) of their underlying quantum fields, which are more fundamental than the particles. Interactions between particles are described by interaction terms in the Lagrangian involving their corresponding quantum fields. Each interaction can be visually represented by Feynman diagrams according to perturbation theory in quantum mechanics.
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...
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...
Using free scalar field for simplicity.
Hi all, I have a question which is pretty simple, we have the path integral in QFT in the presence of a source term:
$$
Z[J] = \int \mathcal{D}\phi \, e^{i \int d^4x \left( \frac{1}{2} \phi(x) A \phi(x) + J(x) \phi(x) \right)}
$$
So far so good. Now...
I am reading the Horatiu Nastase's Introduction to quantum field theory (https://professores.ift.unesp.br/ricardo.matheus/files/courses/2014tqc1/QFT1notes.pdf ) ( Attached file ) or Peskin, Schroeder's quantum field theory book, p.105, (4.77).
Through p.176 ~ p. 177 in the Nastase's Note, he...
Physicist Nima Arkani-Hamed has taken an approach to understand fundamental physics based on geometry (specifically, positive geometry). This started with his work with Jaroslav Trnka in the amplituhedron [1] and later it was generalised to the associahedron [2],the EFT-hedron [3]...
I was...
This isn't a homework problem (it's an example from David Tong's QFT notes where I didn't understand the steps he took), but I am confused as to how exactly to take the partial derivative of the Lagrangian with respect to ##\partial(\partial_\mu \mathcal{A}_\nu)##. (Note the answer is...
What means exactly the principle of 'locality' in context of gauge theory? Motivation: David Tong wrote in his notes on Gauge Theory (p 115): "their paper (the 'original' paper by Yang & Mills introducing their theory) suggests that global symmetries of quantum f ield theory– specifically SU(2)...
In scattering theory, the quantity of interest is the amplitude for the system—initially prepared as a collection of (approximate) momentum eigenstates—to evolve into some other collection of momentum eigenstates. For example, for ##m\to n## scattering, the amplitude we're interested in is...
Confronted with my inability to grasp Witten's Susy QM examples of supersymmetry breaking, I concluded that the problem was that I was not understanding spontaneous symmetry breaking in simpler contexts.
It seems that SSB is not possible in QM because of tunneling between the different states...
When it comes to scattering in QED it seems only scattering cross sections and decay rates are calculated. Why is that does anyone calculate the actual evolution of the field states or operators themselves like how the particles and fields evolve throughout a scattering process not just...
Hi
Would you explain to me what is the q^ and how they are related to completeness.How can i solve this exercise?It is from "Quarks and leptons An Introductory course in Modern Particle Physics" of Halzen and Alan D.Martin.Also, can you point me to a useful bibliography?
This is the defining generator of the Lorentz group
which is then divided into subgroups for rotations and boosts
And I then want to find the commutation relation [J_m, J_n] (and [J_m, K_n] ). I'm following this derivation, but am having a hard time to understand all the steps:
especially...
I am a bit confused on how we can just say that (z',p) form a 4-vector. In my head, four vectors are sacred objects that are Lorentz covariant, but now we introduced some new variable and say it forms a 4-vector with momentum. I understand that these are just integration variables but I still do...
I'm trying to apply an operator to a massless and minimally coupled squeezed state. I have defined my state as $$\phi=\sum_k\left(a_kf_k+a^\dagger_kf^*_k\right)$$, where the ak operators are ladder operators and fk is the mode function $$f_k=\frac{1}{\sqrt{2L^3\omega}}e^{ik_\mu x^\mu}$$...
What is the Schrodinger equation in QFT? is it the nonrelativistic approximation of a Klein-Gordon scalar field? or Is there more?
I have read that the Schrodinger equation describes a QFT in 0 dimensions.
I accept every answer
It is often argued that Dirac Equation is not valid as relativistic quantum mechanics requires the creation of antiparticles. But, there are also some arguments that suggest otherwise. For example, I saw Arnold Neumaier's website on this that there are multiparticle relativistic quantum...