QFT on a Lattice: Researching Lattice Field Theory

In summary, lattice QCD is a very interesting field that is still being explored with modern technology.
  • #1
gnl
21
0
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?
 
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  • #2
Sure, I only know the basic theory behind quantum computing rather than the practicalities, how is the problem of decoherence being overcome?
 
  • #3
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...
 
  • #4
Sorry I misread your post, i thought you were taliking about QFT computing
 
  • #5
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!
 
  • #6
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.
 
  • #7
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?
 
  • #8
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!
 

1. What is lattice field theory?

Lattice field theory is a computational approach used in theoretical physics to study quantum field theories. It involves discretizing space and time into a lattice and using numerical simulations to calculate the properties of the theory.

2. Why is lattice field theory important?

Lattice field theory allows researchers to study quantum field theories that cannot be solved analytically, such as quantum chromodynamics (QCD). It also provides a way to test theories and make predictions that can be compared to experimental results.

3. How is lattice field theory different from other approaches?

Lattice field theory is a non-perturbative approach, meaning it does not rely on approximations or expansions. It also takes into account the discrete nature of space and time, which is important for studying certain phenomena, such as confinement in QCD.

4. What are the limitations of lattice field theory?

One of the main limitations of lattice field theory is its reliance on numerical simulations, which can be computationally expensive and time-consuming. It also has difficulty incorporating certain types of symmetries and can be limited in its ability to study systems at high energies.

5. What are some current research topics in lattice field theory?

Some current research topics in lattice field theory include studying the phase diagram of QCD at finite temperature and density, exploring the properties of strongly interacting matter, and investigating new approaches to improve the efficiency of numerical simulations.

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