Saadiyat island. The view from my window is across the desert to the Persian Gulf.

Have just been discussing with my colleague Dan Grady here the issue of boosting the pull-push quantization via stable homotopy types to pQFT. Maybe there is a way…

]]>Great! Will you be out there on campus much of the time?

]]>Yes, so I need to get some backlog of referee reports and my contribution to “New Spaces…” out of the way, then I am free.

I am on academic leave at NYUAD now, for about two years, with no obligations besides research.

]]>I hope you get to teach the course again. It’s a great luxury being able to improve a course incrementally from year to year. I hate to think of the number of once-delivered courses I ran from the early days.

Can you get back to research now?

]]>For the time being I’ll declare *A first idea of quantum field theory* done.

I did not manage to write the last intended chapter 17. on QED, and without that a bunch of examples are missing. I hope to get back to this, but for the moment I need to focus on other tasks.

Also, there are little remaining gaps and probably mistakes. I’ll keep an eye on it and will try to incrementally optimize things. But for the moment I need a break.

]]>I am now preparing chapter *16. Renormalization* from the material that I have been compiling in the entry *renormalization*.

What is still missing is example computations. I have to see if I find time for that.

]]>Hmm your multiplying-by-$\theta$-business above seems to be on the $Obs$ industry instead of the $\Gamma_\Sigma(E)$ industry I was asking. But the same business goes on for the latter? My guess is an “even-degree-to-even-degree” plot

$\Psi_{(-)}: \mathbb{R}^n \rightarrow \Gamma_\Sigma(E_{even})$(or rather

$\Psi_{(-)}: \mathbb{R}^{n+p+1} \rightarrow E_{even}$) that dually takes an even coordinate $\psi^a \in C^\infty (E_{even})$ to an even coordinate $x\in C^\infty( \mathbb{R}^{n+p+1})$ corresponds to an “odd-degree-to-odd-degree” plot

$\Phi_{(-)}: \mathbb{R}^{n|1} \to \Gamma_\Sigma(E_{odd})$(or rather

$\Phi_{(-)}: \mathbb{R}^{p+n+1|1} \to E_{odd}$that takes an odd coordinate $(\psi^a)^\ast \in C^\infty(E_{odd} )$ (which is dual to $\psi^a$) to an odd coordinate $\theta x \in C^\infty(\mathbb{R}^{p+n+1|1} )$. This could justify denoting $\Phi_{(-)}$ by $\theta \Psi_{(-)}$ (which is the reverse direction of the old notation.)

(Thank you. The tedious method is good enough for me, as I was only troubled by not knowing a general way to get the link. No, those two were all I did send. I will be posting more and more questions tonight and the coming days.)

]]>I have sprayed a few new questions on the PhysicsForum.

Thanks. I see one question, here. Did you send more?

]]>By the way, is there any general strategy to obtain a link to a specific paragraph in a nLab’s article? So far, my method is to search for a hyper-mentioning of the Def/Prop./Theorem to extract its address.

Unfortunately there is no good way to do this.

What you can do is go to the source of the page by replacing “…/show/…” in the URL with “…/source/…”, then find your paragraph there and see if it is equipped with an anchor of the form

```
#AnchorName
```

That’s how I pointed to a paragraph in message #69 above. But it’s a bit tedious…

]]>The multiplying-by-$\theta$-business comes from using the natural bijection between maps of the form

$\mathbb{R}^{0\vert 1} \longrightarrow [ \Gamma_{\Sigma}(E), \mathbb{C} ]$with maps of the form

$\mathbb{R}^{0\vert 1} \times \Gamma_\Sigma(E) \longrightarrow \mathbb{C}$By pullback, these need to take the canonical even coordinate $c$ on $\mathbb{C}$ to an *even* coordinate on the Cartesian product $\mathbb{R}^{0\vert 1} \times \Gamma_\Sigma(E)$.

Now if $E = \Sigma \times S_{odd}$, then the *odd* coordinates of $\Gamma_\Sigma(E)$ are the $\mathbf{\Psi}^ \alpha(x)$, regarded in odd degree. But on the Cartesian product with $\mathbb{R}^{0\vert 1}$ we may multiply these with the canonical odd coordinate $\theta$ on $\mathbb{R}^{0 \vert 1}$ to get the even element $\theta \mathbf{\Psi}^\alpha(x)$:

This is known as “superfield-expansion”.

I have now added a further example to this effect, here.

]]>That would be my pleasure too!

I have sprayed a few new questions on the PhysicsForum. For the above question, I would not have raised it if from the start you had used the current notations. The old notation left an impression on me that the “even-degree-to-even-degree” plot $\Psi_{(-)}: \mathbb{R}^{n} \to \Gamma_\Sigma(E_{even})$ is obtained from “mixed-degree” plot $\Phi_{(-)}: \mathbb{R}^{n|1} \to \Gamma_\Sigma(E_{odd})$ by multiplying $\Phi_{(-)}$ with some odd-degree element $\theta$ (in $\mathbb{R}^{0|1}$?). If this impression is true, then the “multiplying” procedure has not been clear to me.

(By the way, is there any general strategy to obtain a link to a specific paragraph in a nLab’s article? So far, my method is to search for a hyper-mentioning of the Def/Prop./Theorem to extract its address.)

]]>Thanks, great. I’ll try to react to questions in any form, but there might be delays. If you volunteer to type up answers that you extract from what I say verbally, that would be magnificent! Thanks.

]]>Dear Urs,

Yes, I’ve just found out the proper way to display the maths.

Thank you. I will switch to the PhysicsForum and continue there. Also, I forgot to tell you that if it’s more convenient for you to answer my written questions verbally when we meet, please do so and I then could totally post your answers to the forum for the benefit of the participants there (and of mine, as this method could serve as a way for me to check whether I have really got the answers.)

]]>Thanks for your comment.

I assume you are referring to this paragraph?

Looking at it, i see that I used the symbol “$\Psi$” twice, where I should have used two different symbols. I have changed it now, let me know if this clarifies the issue.

(By the way, the source code in your question looks okay, probably what you need to do to make it display properly is to check the box “Markdown+Itex” below the edit pane.)

(Another by the way: when we talked about discussion in “the forum” I was thinking of PhysicsForums, such as here. It’s fine with me either way, but over at PhysicsForums there are more participants interested in quantum field theory, and hence more chance for you to find a useful exchange. )

]]>Dear Urs,

(I am a/the student in your MQFT lecture that often asks questions that are quite of the same content until I realize it. Here are likely another questions of the same nature.)

- I am clear about (the proof of) the 1-1 correspondence between $\{ \mathbb{R}^{n|1} \to \Gamma_\Sigma(E_{odd}) \}$ and $\{ \mathbb{R}^{n} \to \Gamma_\Sigma(E_{even}) \}$. But why do we denote the correspondence of $\psi_{(-)}$ in the former by $\theta\psi_{(-)}$ in the latter?

Now I am finalizing chapter *15. Interacting quantum fields*

This is essentially the material that I have been compiling into the entry *S-matrix* in the section “In causal perturbation theory”.

now I have finalized chapter *14. Free quantum fields*

finally I have finalized chapter *13. Quantization*

Now I am finalizing chapter *12. Gauge fixing*. (This construction lifts the remaining obstruction to quantization by causal perturbation thory, which is finally the topic from chapter 13 on…)

In editing I briefly create or touch various related entries, without however having time at the moment to do these justice as stand-alone entries (I’ll try to come back to this later). For instance here I edited *wave polarization*.

Sorry to interrupt, I will try to avoid posting here after this so that you can get back to the content.

Thanks for your thoughts, I agree with your plan, then I will put this down as something to implement. I will look at the unicode issue first, though.

(Adeel actually made the change, so he deserves the credit, but thanks! :-))-

]]>Thanks to Richard’s admin work, finally we may get back to the content of the entry.

I am finalizing the polishing of chapter 11 “Reduced phase space”. Please let me know how it reads.

]]>Good idea.

Right now I am enjoying the split into smaller separate field. Because even though the big file presumeably saves now, it still means that it needs more than half a minute to do so, while the smaller files save more quickly. Also the big file I have to edit locally in an editor, because my small webbook stalls when trying to edit big files in the nLab edit window; while the small files I can edit here, which is to be preferred.

]]>By the way, Urs, you may prefer to change back your includes now to having the content on the page, so that the user sees something happening. Or, if you prefer, we could look into changing the behaviour of rendering of includes, if people wish. Currently they are ’pre-processed’, i.e. each include finishes processing before the page loads. It looks fairly simple to change things so that includes process on the fly like normal, but we’d need to test it carefully locally first. Let us know if we should look into this.

]]>Yay! The page loads!. A million thanks!!

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