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...
Im following Weinberg's QFT volume I and Im tying to show that the following equation vanishes at large spatial distance of the possible particle clusters (pg 181 eq 4.3.8):
S_{x_1'x_2'... , x_1 x_2}^C = \int d^3p_1' d^3p_2'...d^3p_1d^3p_2...S_{p_1'p_2'... , p_1 p_2}^C \times e^{i p_1' ...
If at high energies the electromagnetic and weak force are combined into one electroweak force, then at high energies, the electrons will not create an electrostatic field and will not repel?
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$$
The equation of motion is ##\partial_\mu F^{\mu\nu}+m^2A^\nu = 0##
Expanding the EOM with the definition of ##F^{\mu\nu}## the Klein-Gordon equation for...
Hey there! I've recently been looking at calculating amplitudes, densities of states and scattering cross sections in QFT, but am having a little bit of trouble with the exact form of the cross section - particularly with factors of ##2E## for the energies of the incoming and outgoing particles...
Hello everybody!
I have a big question about the renormalization: I do not understand why the "renormalization condition" is to impose the tree level result. Now I will explain it better.
Let's take, for example, the electron self energy. The tree-level contribution is the simple fermionic...
Hello everybody!
I was studying the Glashow-Weinberg-Salam theory and I have found this relation:
$$e^{\frac{i\beta}{2}}\,e^{\frac{i\alpha_3}{2} \begin{pmatrix} 1 & 0 \\ 0 & -1 \\ \end{pmatrix}}\, \frac{1}{\sqrt{2}}\begin{pmatrix} 0\\ v \\ \end{pmatrix} =...
The two electrons will be repelled by electrostatic force, but they interact with weak force, means that in addition to the electrostatic force between the electrons there will be weak force?
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##...
If the electron creates an electric field around itself that can be detected,then the electrostatic field is real? So why was not the "virtual" photon found?
What does it mean ?
"the virtual photon's plane wave is seemingly created everywhere in space at once, and destroyed all at once. Therefore, the interaction can happen no matter how far the interacting particles are from each other."
As far as I know, the electrostatic force between two...
1. Homework Statement
Show that, after considering all 1 particle irreducible diagrams, the bare scalar propagator becomes:
$$D_F (p)=\frac{i}{p^2-m^2-\Sigma (p^2)}$$
And that the residue of the pole is shifted to a new value, and beomes...