I am trying to get a foothold on QFT using several books (Lancaster & Blundell, Klauber, Schwichtenberg, Jeevanjee), but sometimes have trouble seeing the forest for all the trees. My problem concerns the equation of QED in the form
$$
\mathcal{L}_{Dirac+Proca+int} =
\bar{\Psi} ( i \gamma_{\mu}...
I was reading about the renormalization of ##\phi^4## theory and it was mentioned that in order to renormalize the 2-point function ##\Gamma^{(2)}(p)## we add the counterterm :
\delta \mathcal{L}_1 = -\dfrac{gm^2}{32\pi \epsilon^2}\phi^2
to the Lagrangian, which should give rise to a...
Hi! I know some theorists believe all quantum fields and gravitational field are different aspects of one universal field. What does that formally (e.g. mathematically) mean "to be different aspects of" and how can one prove, let's say, fields A and B are different aspects of C?
By the way, I...
Hi everyone, I'm new to PF and this is my second post, I'm taking a QFT course this semester and my teacher asked us to obtain:
$$[\Phi(x,t), \dot{\Phi}(y,t) = iZ\delta^3(x-y)]$$
We're using the Otto Nachtman: Elementary Particle Physics but I've seen other books use this notation:
$$[\Phi(x,t)...
Hi everyone, I'm taking a QFT course this semester and we're studying from the Otto Nachtman: Texts and Monographs in Physics textbook, today our teacher asked us to get to the equation:
[Φ(x,t),∂/∂tΦ(y,t)]=iZ∂3(x-y)
But I am unsure of how to get to this, does anyone have any advice or any...
Non-relativistic Bremsstrahlung is discussed classically in Rybicki “Radiative Processes in Astrophysics” where Larmor’s formula is used to find the power radiated in a collision between an electron and a Coulomb field. The Fourier transform of the pulse allows for a description of the pulse in...
Consider the process e^-\rightarrow e^-\gamma depicted in the following Feynman diagram.
The spin-averaged amplitude with linearly polarised photons is
\overline{|M|^2}=8\pi\alpha\left(-g^{\mu\nu}+\epsilon^\mu_+\epsilon^\nu_-+\epsilon^\mu_-\epsilon^\nu_+\right)\left(p_\mu p^\prime_\nu+p_\nu...
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...
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...
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...
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?
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...
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 have always learnt 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...
Nieuwenhuizen uses a method for calculating the propagator by decomposing the field ## h_{\mu\nu}, ## first into symmetric part ## \varphi_{\mu\nu} ## and antisymmetric part ## \psi_{\mu\nu} ##, and then by a spin decomposition using projector operators. Using this he writes the dynamical...
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'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 Electronic Journal of Theoretical Physics 10(28):27–80 · May 2006.
Francis...
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...
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...
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...
When we say energy is applied to that field to create an excitation which is a particle, where does that energy come from and how is it applied? For example on beta decay where a new electron is formed, where does the energy come from the create an excitement in the electron field?
Problem Statement: How does the Higgs field “give mass”
Relevant Equations: The exact way that particles interact with the Higgs field and therefore create mass.
I’m trying to figure out how the Higgs field works, one problem is that while I originally though of the Higgs field like a medium...
Hi all,
I am in a bit of a funny situation where I need to pick up at least a cursory knowledge of QFT and particle physics in the space of two weeks. I borrowed "QFT and the Standard Model" by Schwartz but I have no idea how I should approach it. Ideally I'd pour through every page, but I...
I'm can't seem to figure out how to functionally differentiate a functional such as Z(J)= e^{\frac{i}{2} \int \mathrm{d}^4y \int \mathrm{d}^4x J(y) G_F (x-y) J(x)}
with respect to J(x) . I know the answer is
\frac{\delta Z(J)}{\delta J(x)}= -i \int \mathrm{d}^4y J(y) G(x-y)
but I'm struggling...