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Results tagged with quantum-field-theory
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user 47373
Quantum Field Theory (QFT) is the theoretical framework describing the quantisation of classical fields which allows a Lorentz-invariant formulation of quantum mechanics. QFT is used both in high energy physics as well as condensed matter physics and closely related to statistical field theory. Use this tag for many-body quantum-mechanical problems and the theory of particle physics. Don’t combine with the [quantum-mechanics] tag.
3
votes
1
answer
170
views
Why 1PI graphs are enough to discuss renormalizability?
In quantum field theory, S-matrix elements are connected to observables which we can measure experimentally.
In order to work with a well-defined theory, we need to remove all the divergences and reno …
- 2,237
3
votes
1
answer
176
views
Invariant terms of Chiral Lagrangian
Stupid question.
Consider a global SU(N) theory spontaneously broken. I want to write the EFT of the Goldstone bosons in terms of the field
$$
\Pi = e^{i\pi^a T^a}
$$
where $T^a$ are the SU(N) gene …
- 2,237
2
votes
Accepted
Invariant terms of Chiral Lagrangian
For simplicity, I will denote $\hat{\pi} = \pi^a T^a$.
The invariant trace term is zero. Indeed
$$
\partial_\mu \Pi \cdot \Pi^\dagger = \left(i\partial_\mu \hat
{\pi}\right)\Pi\cdot \Pi^\dagger = \l …
- 2,237
9
votes
1
answer
1k
views
Anomalous Ward Identities and anomalous dimensions
Let us consider an action $S[\phi,\partial\phi]$ which is classically invariant under a transformation group $G$. The associated Noether current $\mathcal{J}^\mu$ is classically conserved, namely $\pa …
- 2,237
4
votes
0
answers
226
views
Dilaton coupling to CFT
I am studying this paper of Luty, Polchinski and Rattazzi about the $a-$theorem in $d=4$ and the possibly allowed RG flow between fixed points of a theory with metric $g_{\mu\nu}$.
First of all, they …
- 2,237
1
vote
Renormalization of a Feynman diagram with zero bare mass
In dimensional regularization, loop integrals which do not depend on physical external momenta are automatically regularized to be zero. This is so because, in absence of a mass scale, the integral is …
- 2,237
2
votes
2
answers
492
views
Are scalar fields defined up to harmonic functions?
Disclaimer: this question may be very stupid. It looks like I am missing some fundamental point.
Let's consider a massive scalar $\pi$
$$
\mathcal{L}_\pi = -\frac{1}{2}(\partial \pi)^2 -\frac{m^2} …
- 2,237
3
votes
Accepted
Understanding renormalizability and bare mass
As I said in the comment, as long as you don't hit singularities for $k^2=0$, the function $I(k^2)$ is completely regular and you can perform the expansion. As well, you can take the one-dimensional i …
- 2,237
5
votes
Accepted
What does soft symmetry breaking physically mean?
This is a matter of terminology and the physics behind it is very simple.
How do we break a symmetry explicitly? As you know, that's enough to add symmetry-breaking operators to the Lagrangian: rele …
- 2,237
0
votes
0
answers
605
views
Propagator with derivative interaction
I work with this interaction Lagrangian density
$$\mathcal{L}_{int} = \mathcal{L}_{int}^{(1)} + \mathcal{L}_{int}^{(2)} + {\mathcal{L}_{int}^{(2)}}^\dagger = ia\bar{\Psi}\gamma^\mu\Psi Z_\mu +ib(\phi …
- 2,237
2
votes
1
answer
628
views
Can I use Pauli-Villars and dimensional regularization together?
There are at least two ways to compute the electron-self energy. You can use Pauli-Villars or dimensional regularization, for example.
On Weinberg's book, it's chosen the first method, while on my le …
- 2,237
2
votes
0
answers
319
views
S-matrix element for forward scattering and amputed green function
I'm studying dispersion relations applied as alternative method to perturbation theory from Weinberg's book (Vol.1)
Let's consider the forward scattering in the lab frame of a massless boson of any s …
- 2,237
4
votes
Vertex factor for $\frac{g}{4} (A_{\nu}A^{\nu})^2$ in QED
You can write the interaction as
$$
\frac{g}{4} A^\rho A^\nu A^\sigma A^\mu g_{\rho \nu} g_{\sigma \mu}
$$
Suppose you have a 4-point function to compute with the following external polarization vec …
- 2,237
8
votes
Accepted
"Dimensional analysis" arguments in quantum field theory
A good way to do dimension analysis in computing amplitudes relies on a good power-counting of the action. Let me explain how it works before answering your question. For simplicity, in the following, …
- 2,237
1
vote
2
answers
417
views
Coupling of a massless vector to a conserved current
In order to describe one-particle states of spin-1 in a Lagrangian description, we need to use a field $A_\mu$. This is a 4-vector up to gauge transformations, which means that under Lorentz transform …
- 2,237