All Questions
8
questions
1
vote
0
answers
40
views
Why is it justified to focus on gauge transformations constant at spatial infinity in QCD instantons?
In the context of Yang-Mills theories and QCD instantons, much of the literature and conventional treatment hinges on the consideration of gauge transformations that remain constant at spatial ...
- 841
0
votes
1
answer
81
views
Theta vacua eigenstates
I have been trying to prove the very simple result that the eigenstates of an operator with matrix elements
$$
\langle n^\prime | H | n \rangle \sim g(|n^\prime-n|),
$$
in a basis $\{|n\rangle\}^{+\...
- 1,742
1
vote
1
answer
506
views
What does the Pontryagin index do in BPST instanton (solution to Yang-Mills theory)?
$$
\mathcal L = -\frac12\mathrm{Tr}\ F_{\mu\nu}F^{\mu\nu}+i\bar\psi\gamma^\mu D_\mu\psi
$$
We take this Lagrangian for QCD, after this I need to calculate BPST instanton with topological Pontryagin ...
2
votes
2
answers
573
views
Understanding the prefactor $\frac{\theta g^2}{32\pi^2}$ of the $F\tilde{F}$ term in Yang-Mills theories
The most general Yang-Mills (YM) action consistent with Lorentz invariance, gauge invariance and renormalizability should contain a term $$\kappa F_{\mu\nu a}\tilde{F}^{\mu\nu a}\tag{1}$$ where $\...
- 26.8k
4
votes
1
answer
393
views
Are theta vacua topologically protected?
In discussions of Yang-Mills instantons it is often stated that one should sum in the path integral over all contributions of fluctuations around all the topologically distinct vacua labelled by ...
- 708
3
votes
1
answer
267
views
Isn't there a unique vacuum of the Yang-Mills quantum theory?
The theta vacua$^1$ of a Yang-Mills quantum theory are given by $$|\theta\rangle=\sum\limits_{n=-\infty}^{\infty}e^{in\theta}|n\rangle.$$ In Srednicki's Quantum Field Theory, he claims that the ...
- 26.8k
3
votes
1
answer
745
views
Is it the chiral anomaly which is solely responsible for having instanton effects (and therefore, the $\theta-$term) in the QCD action?
$\textbf{Fact 1}$ In principle, the QCD Lagrangian should contain a Lorentz invariant, gauge invariant, dimension-4 term $\sim\theta \text{Tr}[F^{\mu\nu}\tilde{F}_{\mu\nu}]$. This term, however, is ...
- 26.8k
4
votes
1
answer
236
views
A Variation on Laplace's equation (context: Yang-Mills N-Instantons, Rajaraman's book)
Statement of the problem
I need to solve the equation
\begin{align}
0 = \frac{1}{\phi} \partial_{\sigma}\partial_{\sigma} \phi \hspace{20mm} (1)
\end{align}
where $\phi$ is a scalar field and we'...
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