QFT on a Lattice: Researching Lattice Field Theory

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Discussion Overview

The discussion revolves around the application of quantum field theory (QFT) on a lattice, particularly in the context of lattice field theory and its computational aspects. Participants explore various topics including lattice QCD, numerical methods for evaluating Green's functions, and the challenges of non-perturbative aspects of QCD.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant expresses interest in QFT on a lattice and invites others to discuss.
  • Another participant raises a question about overcoming decoherence in quantum computing, indicating a potential misunderstanding of the topic.
  • A participant discusses the process of writing a discrete version of the action in Euclidean space-time and using numerical methods to evaluate Green's functions, noting the role of inverse lattice spacing as a momentum cutoff.
  • One participant mentions the complexity of QCD and its non-perturbative aspects, highlighting the lattice as a method to study confinement and hadron structure.
  • Another participant inquires about the original poster's specific research topic and whether it involves Monte Carlo estimations of path integrals.
  • The original poster shares their focus on lattice QCD, detailing their work on hadron spectroscopy and the study of leptonic and semileptonic decays, which involve non-perturbative quantities.
  • There is a mention of the computational demands of lattice QCD, with a note that interesting physics can still be explored using scalar models.

Areas of Agreement / Disagreement

Participants express interest in the topic and share related experiences, but there is no consensus on specific methodologies or challenges faced in lattice QFT research. Multiple perspectives on the application and implications of lattice QCD are presented.

Contextual Notes

Some participants reference specific techniques and challenges in lattice QCD, such as the need for significant computational resources and the nature of non-perturbative calculations, but these points remain open for further exploration and discussion.

gnl
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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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Sure, I only know the basic theory behind quantum computing rather than the practicalities, how is the problem of decoherence being overcome?
 
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...
 
Sorry I misread your post, i thought you were taliking about QFT computing
 
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!
 
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.
 
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?
 
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!
 

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