general physics motivations for numerical simulations of quantum field theory

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1、LAUR-99-789GeneralPhysicsMotivationsforNumericalSimulationsofQuantumFieldTheoryR.Gupta1TheoreticalDivision,LosAlamosNationalLaboratory,LosAlamos,NM87545,USAAbstractInthisintroductoryarticleabriefdescriptionofQuantumFieldTheories(QFT)ispresentedwithemphasisonthedistinctionbetweenstronglyandweaklyc

2、oupledtheories.AcaseismadeforusingnumericalsimulationstosolveQCD,theregnanttheorydescribingtheinteractionsbetweenquarksandgluons.Ipresentanoverviewofwhatthesecalculationsinvolve,whytheyarehard,andwhytheyaretailormadeforparallelcomputers.Finally,Itrytocommunicatetheexcitementamongstthepractitioner

3、sbygivingexamplesofthequantitieswewillbeabletocalculatetowithinafewpercentaccuracyinthenextfiveyears.Keywords:QuantumFieldtheory,latticeQCD,non-perturbativemethods,parallelcomputersarXiv:hep-lat/9905027v120May19991IntroductionThecomplexityofphysicalproblemsincreaseswiththenumberofdegreesoffreedom,

4、andwiththedetailsoftheinteractionsbetweenthem.Thisincreaseinthenumberofdegreesoffreedomintroducesthenotionofaverylargerangeoflengthscales.Asimpleillustrationiswaterintheoceans.Thebasicdegreesoffreedomarethewatermolecules(∼10−8cm),andthelargestscaleistheearth’sdiameter(∼104km),i.e.therangeofscales

5、span1017ordersofmagnitude.Wavesintheoceancovertherangefromcentimeters,tometers,tocurrentsthatpersistforthousandsofkilometers,andfinallytotidesthatareglobalinextent.Solutionstomodelingthebehaviorofoceanwavesdependsonwhetherthiswholerangeofscalesareimportantorwhetheronecanisolate1rajan@lanl.govPrepr

6、intsubmittedtoElsevierPreprintVERSION—1February2008them.Forexample,tounderstandthecurrentsandtidesonedoesnotneedtoknowthemolecularnatureofwateratall,onecantreatitasacontinuousfluid.Ingeneral,differenttechniquesarenecessarydependingonwhetherdisparatelengthscalesarestronglyorweaklycoupled.Thestudyofi

7、nteractionsbetweenelementaryparticlesinvolveslengthscales(<10−13cm)wherequantumeffectsarelarge.Thequantumvacuumisnolongerasmoothplacidentity,butmorelikeafrothingbubblingpotofstew.Ithasfluctuationsatallscalesfrom10−13cmto