## Thursday, February 21, 2008

### Word on the arXiv

The arXiv have announced that they now support submissions of "Microsoft Word DOCX or other OOXML (Office Open XML) document[s]". While I am perfectly aware that high-energy physicists (or indeed any kind of physicists) are not the only users of the arXiv, and that usage of TeX is not terribly common outside the physics/mathematics field (though I know a few philosophers and economists, and even one historian, who were won over by the superior look of texts typeset in LaTeX), I find this a little worrying, especially given that the arXiv acknowledges support from the Microsoft Technical Computing Initiative. What worries me is the possibility that this might be the first step towards a less open information architecture at the arXiv, and by implication in the high-energy physics communications sector. Will Microsoft try to gain a foothold, leading to the eventual establishment of their "open" (not) formats as the only accepted submission and download format? One sincerely hopes not.

Labels:
arXiv

## Thursday, February 14, 2008

### arXiv catchup

I have been too ~~lazy~~busy recently to blog anything. However, in the spirit of the day, I'd like to share a romantic little poem extolling the nonabelian nature of strong attraction:

No, I won't give up physics and become a card designer for H$llm$rk, don't worry. But after softening your hearts with this touching verse, I'd like to blog about some rather old stuff, which I hope hasn't gone stale in the meantime.

One paper on the arXiv that struck me as interesting in the last couple of months was this paper by Jeffrey Mandula (of Coleman-Mandula No-Go fame), who discusses the consequences of Lüscher's nonlinear realisation of chiral symmetry for Ginsparg-Wilson fermions. We recall that this symmetry can be written in two inequivalent ways by putting the phase factor e

Another interesting paper was this one by Mike Creutz who proposed a new fermion discretisation based on features of the electronic structure of graphene. Apparently the low electronic excitations of a grpahene layer are described by the massless Dirac equation, and a lattice model based on this (by reducing the links in one of the three graphene hexagonal directions to points, and rescaling eveything to make the lattice rectangular again) exploits this to achieve the minimum number (two) of doublers permitted in an conventional chiral lattice theory by the Nielsen-Ninomiya theorem, and this construction can be extended to four dimensions and gauged to get a lattice discretisation of QCD with two light quark flavours. This was quickly followed up by a similar proposal for a minimally-doubling quark action, and by this paper which shows that any minimally-doubling chiral lattice theory necessarily has to break either of the discrete symmetries P or T such that their product PT is broken; this allows the generation of additional (relevant) dimension 3 operators that have to be removed by fine-tuning, precluding the use of minimally-doubling chiral actions in practice (unless some additional non-standard symmetry should conspire to do that fine-tuning itself, a possibility hinted at in the conclusion).

Roses are red, violets are blue

quarks come in colours, and so does glue.

No, I won't give up physics and become a card designer for H$llm$rk, don't worry. But after softening your hearts with this touching verse, I'd like to blog about some rather old stuff, which I hope hasn't gone stale in the meantime.

One paper on the arXiv that struck me as interesting in the last couple of months was this paper by Jeffrey Mandula (of Coleman-Mandula No-Go fame), who discusses the consequences of Lüscher's nonlinear realisation of chiral symmetry for Ginsparg-Wilson fermions. We recall that this symmetry can be written in two inequivalent ways by putting the phase factor e

^{iαγ5}either on the quark field ψ or its conjugate $$\bar{\psi}$$. The crucial fact that Mandula points out is that both of these are independent symmetries of the lattice theory, and they don't commute! Hence, we have to look for the symmetry algebra generated by them, which turns out to be infinite-dimensional. Hence the lattice symmetry has an infinite number of conserved currents, a structure quite different from the continuum theory. However, it would really appear that the differences between any two of these lattice currents are just lattice artifacts of order*a*or higher that should disappear in the continuum limit, if the latter is properly defined. So some of the objections that the paper raises are likely a lot less serious than stated (especially the non-locality exhibited for free overlap fermions [eq. (38)] goes away once one realises that the continuum limit must be taken with the negative mass*s*constant in*lattice*units), but it appears that Ginsparg-Wilson fermions may have their own set of problems beyond just being expensive to simulate. Any comments on this from Ginsparg-Wilson specialists would be of great interest.Another interesting paper was this one by Mike Creutz who proposed a new fermion discretisation based on features of the electronic structure of graphene. Apparently the low electronic excitations of a grpahene layer are described by the massless Dirac equation, and a lattice model based on this (by reducing the links in one of the three graphene hexagonal directions to points, and rescaling eveything to make the lattice rectangular again) exploits this to achieve the minimum number (two) of doublers permitted in an conventional chiral lattice theory by the Nielsen-Ninomiya theorem, and this construction can be extended to four dimensions and gauged to get a lattice discretisation of QCD with two light quark flavours. This was quickly followed up by a similar proposal for a minimally-doubling quark action, and by this paper which shows that any minimally-doubling chiral lattice theory necessarily has to break either of the discrete symmetries P or T such that their product PT is broken; this allows the generation of additional (relevant) dimension 3 operators that have to be removed by fine-tuning, precluding the use of minimally-doubling chiral actions in practice (unless some additional non-standard symmetry should conspire to do that fine-tuning itself, a possibility hinted at in the conclusion).

Labels:
arXiv,
lattice fermions

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