Lattice Field Theory

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?

 

lattice

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...

 

Lattice QCD

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.

 

my field

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!