Musings

I love threaded comments. When I visit an old blog entry, it’s great to have the comments organized thematically, with responses threaded with the comments that inspired them.

On the other hand, while a comment thread is developing, there can be several parallel conversations happening at once. And it can be hard to figure out, from the threaded view, where the new comments are. A chronological view would be more convenient. Of course, you can always subscribe to my comment feed, but that’s not quite the same thing.

Fixing this has been a low-priority item on my TODO list for a long time. Finally, one of my commenters spurred me into action. Thanks to my previous experiments in DOM-wrangling, it was fairly easy to whip together something that would toggle between the default threaded-view and a chronological view (with trackbacks followed by comments, in chronological order).

I haven’t tested it yet in a wide variety of browsers. So, if you encounter problems with it, please let me know.

Over at Cosmic Variance, in a long, and somewhat histrionic comment thread, Lee Smolin makes a new (to me, at least) claim about LQG

LQG easily incorporates most proposals for beyond the standard model unification including supersymmetry.

Since I’m afraid it will get buried over there, I thought I would drag the discussion of this rather important physics point over here. Hopefully, some LQG experts can chime in and explain Lee’s statement.

1. What classes of quantum field theories can be incorporated in LQG and what classes cannot?
2. In what sense do the former constitute “most”?
3. In light of the fact that “most” can be coupled to LQG, how are we to deal with Georgi’s objection (which is discussed at greater length here) ?

In the same comment, Lee also says

… someone might earn a Clay prize by rigorously constructing quantum Yang-Mills within LQG. It will certainly not be me, but there are people working on exactly that program. The conjecture is that background independent QFTs are more likely to exist rigorously in 3+1 dimensions than Poincare invariant QFTs.

It would also be interesting for someone to chime in with an explanation of the intuition for why coupling to quantum gravity should make the problem of constructing quantum Yang Mills theory easier, rather than harder.

The number of vacua in an $\mathcal{N}=1$ supersymmetric field theory is, generically, dictated by the Witten index. This number is robust against perturbations, which makes dynamically breaking supersymmetry a challenge. One needs to start with a theory whose Witten index vanishes, and one needs to hope that the dynamical effect which break supersymmetry do not lead to runaway behaviour (like the runaway behaviour in supersymmetric QCD with $N_f \lt N_c$).

One of the nice insights of recent years is that we are not necessarily interested in true vacua (global minima of the effective potential). We might just as well be living in a metastable “false vacuum”, provided its lifetime is long enough. And, despite the paucity of true vacua (absent some symmetry), generic field theories can be chock-a-block with metastable vacua.

Bugs, bugs, bugs. It seems there’s always something to fix.

Since itex2MML 1.1.3, I’ve fixed the following:

In a recent post, I talked a bit about what the mathematicians call “Topological T-Duality.” I posed the question as to how confident we were that their definition is right. A discussion ensued about what “being right” means in this context, and what the implications might be if the definition of Mathai, Bunke and others isn’t right.

Aggregating and republishing over two dozen feeds, of varied provenance, is not without its pitfalls. Wordpress.com’s atom feed templates are somewhat problematic. As a consequence, some of Tommaso Dorigo’s posts were filled with doubly-escaped entities. Fortunately, Sam came through with a fix. Georg von Hippel’s Tex → PNG software plays poorly with Blogger. The latter inserts <br />s into the alt attributes of the created images, which can cause BeautifulSoup to cough up a hairball where the PNG image should be (hopefully fixed now).

But, for the most part, the results look pretty good¹. Some further tweaks, however, made it look even better.

It is enlightened practice to separate styling information from the markup of your document, and place the former in an external CSS stylesheet. An aggregator, like Planet Musings takes blog entries from a variety of sources, and republishes them with a consistent style.

But, sometimes, something essential gets lost in ignoring the external stylesheets of the original sources. That’s where the “Accommodations” section of our stylesheet comes in.

For instance, Cosmic Variance uses CSS classes like class="alignright" and class="alignleft" to float images. Adding directives like

.alignleft { float:left }

made their entries “look right.” On similar grounds, adding

img.mathlogo, img.svglogo { float:right; border:0 }

makes the entries from Musings and The String Coffee Table look more pleasing.

More interesting, though, is the CSS styling of Math, tidbits of which have accumulated, over the years, in the stylesheets of Musings and The String Coffee Table. Now I had to think about which of those bits are actually important enough to merge into the “Accommodations” section of the Planet Musings stylesheet. So I thought I’d share some tips on styling MathML.

Browsers have a nasty habit of introducing linebreaks into inline equations, which (from a mathematical typography point-of-view) is just wrong. To suppress that,

math { white-space: nowrap }

Display equations are sometimes too wide for the viewport. There are various ways to fix that. The one I like is

math[display=block] {overflow:auto;}

Hyperlinks in equations should be styled in some fashion consistent with the styling of hyperlinks in the text. That’s actually quite tricky; the solution involves applying styles to

.news .content :link  { ...}
.news .content :visited { ...}

and, perhaps, also to

.news .content :link:hover  { ...}
.news .content :visited:hover { ...}

etc.

At least some browsers don’t have a default styling for <merror>. Not that anyone desires itex2MML parsing errors to end up in a syndicated feed. But, if there is an error, you’d like to be able to see it:

merror {display:inline;font-size:1em;}

Finally, not strictly a MathML tip, but around here, equation numbers are achieved with a floating <div class="eqno">, which needs a

.eqno {float:right}

Thanks to Sam’s hard work, adding Atom support and MathML support and … to Planet, I decided it was finally time to give it a whirl. Installation was a breeze¹, a few tweaks to the templates, and … the most tedious part was copying the feed URLs I wanted to syndicate into config.ini.

Introducing my very own Physics-oriented “river of news”: Planet Musings. If you’d rather view it in your feedreader, there’s an atom feed, too.

Meanwhile, I quietly released a couple of bugfix revisions to itex2MML, which is now at version 1.1.3.2.

I thought I’d take some time out for a little tour around the physics blogosphere. While there’s plenty of sturm und drang to be found in the usual places, there is also also some really nifty and worthwhile stuff out there

Georg, over at Life on the Lattice has a nice post on NRQCD on the lattice. In studying heavy quark bound states on the lattice, it is often very convenient to replace the Wilson (or Kogut-Susskind) action for the fermions with its non-relativistic counterpart. Obviously, halving the number of degrees of freedom simplifies the task of computing a fermi determinant. But that’s not where the saving really lies. It’s really in removing the rest-energy contribution to the Hamiltonian, (which, otherwise would dominate the decay of Euclidean correlation functions, $C(t,0) \sim e^{-m t}$) that makes the nonrelativistic approximation worthwhile.

I’d love to hear more about the tradeoffs in tuning the higher-order terms in the NRQCD Lagrangian and what the added complexity buys you, in terms of better numerical stability and faster convergence to the continuum.

Urs has a series of posts on Mathai’s approach to the “topological” aspects of T-duality. How T-duality acts on the K-theory of $M\times T^n$ is more-or-less understood. Mathai would like to bootstrap this to some statement about the algebra of functions $C(M\times T^n)$ (in which the K-theory is the algebraic K-theory of modules over this algebra).

Personally, I’m rather dubious of the approach, in that T-duality is more naturally described in terms of the loop space of $X$, rather than $X$ itself (remember, it exchanges momenta and windings). It’s neat, but somehow seemingly accidental, that it reduces to a simple mapping of the K-theories of $X$ and its T-dual.

Travis Stewart reports that the LHC’s ATLAS detector has seen cosmic ray events, an excellent sign that things are working as they should.

Mike Schmitt and Tomasso Dorigo have some posts about techniques for tagging b-jets.

Finally, on a more elmentary level, Dmitri Terryn has a nice little post about the elastic electromagnetic scattering cross-section, from its nonrelativistic, classical expression (Rutherford scattering) to its more complicated, fully quantum-mechanical variations.

Unable to leave well enough alone, I tinkered some more with itex2MML. The latest version does the following:

1. Because of MathML’s strange inheritance rules for the <mi> element, \mathrm{a} did not, as you might expect, produce an upright $\mathrm{a}$, but instead produced an $a$. Now it does the right thing.
2. I purged itex2MML of the deprecated fontstyle and fontweight attributes, substituting the preferred mathvariant attribute instead.
3. I added \tfrac{·}{·}, the AMSLaTeX synonym for {\textstyle \frac{·}{·}}

4. With much trepidation, I added colour support, in the form of \color and \bgcolor. Hideous, inaccessible, things are — of course — possible. (I will resist the temptation to link to some examples.) But a judicious use of colour need not always be bad.

   $$\bgcolor{#DEF}\: x(t)= x_0 \color{purple} e^{-\gamma t} \color{red} \cos({\color{blue}\omega} t)\:$$

   is produced by

   $$
   \bgcolor{#DEF}\:
   x(t) = x_0 \color{purple} e^{-\gamma t}
   \color{red} \cos({\color{blue}\omega} t)\:
   $$

To enable the colour features in comments required yet another re-jiggering of our sanitize spec.

Oh, and the rendering bug on MacOSX, which screwed up \overline? Fixed that.