Editing Lattice gauge theory (section)

==Measurements and calculations==
[[File:Fluxtube_meson.png|thumb|150px|This result of a [[Lattice QCD]] computation shows a [[meson]], composed out of a quark and an antiquark. (After M. Cardoso et al.<ref>{{cite journal | last1=Cardoso | first1=M. | last2=Cardoso | first2=N. | last3=Bicudo | first3=P. | title=Lattice QCD computation of the color fields for the static hybrid quark-gluon-antiquark system, and microscopic study of the Casimir scaling | journal=Physical Review D | volume=81 | issue=3 | date=2010-02-03 | issn=1550-7998 | doi=10.1103/physrevd.81.034504 | page=034504|arxiv=0912.3181| bibcode=2010PhRvD..81c4504C | s2cid=119216789 }}</ref>)]]

Quantities such as particle masses are stochastically calculated using techniques such as the [[Monte Carlo method]].  Gauge field configurations are generated with [[probability|probabilities]] proportional to <math>e^{-\beta S}</math>, where <math>S</math> is the lattice action and <math>\beta</math> is related to the lattice spacing <math>a</math>.  The quantity of interest is calculated for each configuration, and averaged.  Calculations are often repeated at different lattice spacings <math>a</math> so that the result can be [[extrapolation|extrapolated]] to the continuum, <math>a \to 0</math>.

Such calculations are often extremely computationally intensive, and can require the use of the largest available [[supercomputer]]s.  To reduce the computational burden, the so-called [[quenched approximation]] can be used, in which the fermionic fields are treated as non-dynamic "frozen" variables.  While this was common in early lattice QCD calculations, "dynamical" fermions are now standard.<ref>{{cite journal | author=A. Bazavov| title=Nonperturbative QCD simulations with 2+1 flavors of improved staggered quarks | journal=Reviews of Modern Physics | volume=82 | issue=2 | year=2010 | pages=1349–1417 | doi=10.1103/RevModPhys.82.1349 | arxiv=0903.3598 | bibcode=2010RvMP...82.1349B| s2cid=119259340 |display-authors=etal}}</ref>  These simulations typically utilize algorithms based upon [[molecular dynamics]] or [[microcanonical ensemble]] algorithms.<ref>{{cite journal | author=[[David Callaway|David J. E. Callaway]] and [[Aneesur Rahman]] | title=Microcanonical Ensemble Formulation of Lattice Gauge Theory | journal=Physical Review Letters | volume=49 | year=1982 | issue=9 |pages=613–616 | doi=10.1103/PhysRevLett.49.613 | bibcode=1982PhRvL..49..613C}}</ref><ref>{{cite journal | author=[[David Callaway|David J. E. Callaway]] and [[Aneesur Rahman]] | title=Lattice gauge theory in the microcanonical ensemble | journal=Physical Review | volume=D28 |year=1983 | issue=6 | pages=1506–1514 | doi=10.1103/PhysRevD.28.1506|bibcode = 1983PhRvD..28.1506C | url=https://cds.cern.ch/record/144746/files/PhysRevD.28.1506.pdf }}</ref> An alternative method could be simulations on [[Quantum computing|quantum computers]].<ref>{{Cite journal |last=Meth |first=Michael |last2=Zhang |first2=Jinglei |last3=Haase |first3=Jan F. |last4=Edmunds |first4=Claire |last5=Postler |first5=Lukas |last6=Jena |first6=Andrew J. |last7=Steiner |first7=Alex |last8=Dellantonio |first8=Luca |last9=Blatt |first9=Rainer |last10=Zoller |first10=Peter |last11=Monz |first11=Thomas |last12=Schindler |first12=Philipp |last13=Muschik |first13=Christine |last14=Ringbauer |first14=Martin |date=2025-03-25 |title=Simulating two-dimensional lattice gauge theories on a qudit quantum computer |url=https://www.nature.com/articles/s41567-025-02797-w |journal=Nature Physics |language=en |pages=1–7 |doi=10.1038/s41567-025-02797-w |issn=1745-2481|doi-access=free |pmc=11999872 }}</ref>

The results of lattice QCD computations show e.g. that in a meson not only the particles (quarks and antiquarks), but also the "[[Flux tube|fluxtube]]s" of the gluon fields are important.{{citation needed|date=April 2025}}