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1、Fortschr.Phys.61,No.6,685700(2013)/DOI10.1002/prop.201200139Implicationsofminimum-lengthdeformedquantummechanicsforQFT/QG∗MichaelMaziashvili∗∗CenterforElementaryParticlePhysics,ITP,IliaStateUniversity,3/5CholokashviliAve.,Tbilisi0162,∗∗∗GeorgiaReceived23October2012,
2、accepted27November2012Publishedonline8January2013Afterpickingoutwhatmayseemmorerealisticminimalgravitationaldeformationofquantummechanics,westudyitsbackreactionongravity.ThelargedistancebehaviourofNewtonianpotentialcoincideswiththeresultobtainedbyusingofeffectivefiel
3、dtheoryapproachtogeneralrelativity(thecorrectionprovestobeofrepulsivenature).TheshortdistancecorrectionsresultinPlanckmassblackholeremnantswithzerotemperature.Thedeformationofposition-momentumuncertaintyrelationsleadstothesuperluminalmotionthatcanbeavoidedbymakingsi
4、milardeformationoftime-energyuncertaintyrelation.SuchdeformationalsoavoidsUVdivergencesinQFT.c2013WILEY-VCHVerlagGmbH&Co.KGaA,Weinheim1IntroductionNowadays,theultimatetheoryofquantumgravityisstillunderconstruction.Nevertheless,thereareseveraldifferentsuccessfulappr
5、oachestoquantumgravity,eachofthesehavingcertainadvantagesovertheothersforstudyingofaconcretequestion[1].Anunifyingframeworkawaitsitsdiscovery.Thepresentarticlemainlyfocussesonaphenomenologicaldiscussionofminimum-lengthdeformeduncertaintyre-lations.Astheconceptofmini
6、mumlengthnaturallyappearsinallapproachestoquantumgravity,onemighthopethatthebottom-upstudybyincorporatingofminimumlengthintoquantummechanicsmayshowupagooddealofknowledgeaboutquantumgravity.Orotherwisespeaking,theminimumlengthdeformedquantummechanicsmayprovetobeavery
7、economicandatthesametimequitepredictiveunifyingframeworkfordiscussingquantumgravitationaleffects.Itisevidentthateveninthesimplestcasethereisagooddealoffreedominpossibleminimum-lengthdeformationsofposition-momentumuncertaintyrelations(s).Inthebeginningwepointoutthato
8、neofthemisnaturallysingledoutandprovidefurthermotivationforit.Indeed,forthissortofmodificationthereareseveralwellknownGedankenexperimentapp
