Lattice Field Theory

[gnl]

Hi everyone! I would like to post a new thread, related to my research work: QFT on a lattice, i.e. on computers! Is anyone interested?

[jcsd]

Sure, I only know the basic theory behind quantum computing rather than the practicalities, how is the problem of decoherence being overcome?

[gnl]

This is what I am talking about. Take some QFT. Write a Euclidean space-time discrete version of the action and then use numerical methods to evaluate Green´s functions. The inverse lattice spacing serves as a momentum cutoff...

[jcsd]

Sorry I misread your post, i thought you were taliking about QFT computing [g)]

[selfAdjoint]

This is certainly a very interesting and hot topic, and the opportunity to get some info from the horse's mouth is not to be missed. Fire away, gnl!

[gnl]

One of the most interesting field theories to be studied on the lattice is QCD. QCD is a very complicated theory, with many non-perturbative aspects. The lattice offers a way to investigate, from first principles, such aspects. In the low-energy regime, the QCD coupling becomes too large for any perturbative expansion to make sense. Confinement and hadron structure are among the things one can study in Lattice QCD: hadron masses (QCD spectroscopy in general, including glueballs), hadronic matrix elements.

A good intro can be found in:
hep-lat/9807028

Agreement with experiment has been striking in many cases.

[selfAdjoint]

I am working my way through the tutorial, and I wondered, gnl what is your topic? And are you going to be doing monte carlo estimations of path integrals like it says?

[gnl]

My field of research, so far, has been lattice QCD. I have done works on hadron spectroscopy and on the study of leptonic anc semileptonic decays. These decays involve some non-perturbative quantity, like decay constants or form factors.

These objects are calculated as MC estimates (numerical path integral!) of time-ordered products of fields. For example, given the operator that creates a meson with given quantum numbers from the vacuum, one that creates another meson , and a current, lots of things can be calculated.

Lattice QCD needs BIG CPUS!!! However, lots of interesting physics can still be explored with scalar models. The Higgs boson, after all, is such a field!