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1、ACOLLECTIONOFEXERCISESINTWO-DIMENSIONALPHYSICSPARTICOSTASJ.EFTHIMIOUNewmanLaboratoryofNuclearStudiesCORNELLUNIVERSITY&FLORIDASOUTHERNCOLLEGEDONALDA.SPECTORDepartmentofPhysicsHOBART&WILLIAMSMITHCOLLEGESarXiv:hep-th/0003190v122Mar2000RELEASE:1.0CornellCLNS99/1612cAllrightsreserved.This
2、bookwastypesetinTEXusingtheLATEX2"DocumentPreparationSystem.PROLEGOMENAADEFENSEFORTWODIMENSIONSorANEXTRAORDINARYPREFACEInhisclassicbookFlatland[1],E.A.Abbottdescribedanimaginarytwo-dimensionalworld,embeddedinthreedimensions,andpopulatedbytwo-dimensional guresthatthink,speak,andhaveal
3、lthehumanemotions.Theauthor,aschoolmasterwithaclassicsback-groundwhowasinterestedinliteratureandtheology,wrotehisscience ctionfantasyinpuremathematicsforentertainment.Hepublisheditunderapseudonymtoavoidanynegativecriticismresultingfromitre
ectingpoorlyonhismoreformalworks.Apparently,
4、heneverimaginedthatthisworknotonlywouldentertainmanygenerationsofphysicistsandmathematicians,butalsowouldcontainconceptsthatfuturescientistswouldworkon.Almost120yearsafterFlatlandwaswritten1,muchhashappenedtoourideasandconceptsofspaceswithvariousdimensions.Relativityplacedhumansinafo
5、ur-dimensionalspace-time;morerecently,StringTheoryclaimsthatthedimensionalityofouruniversehastobeupdatedto10or11dimensions.Wehavethuslearnttofeelcomfortableinaspaceofmanydimensions.Wehavealsobecomemorecomfortableinspacesoffewdimensions.Two-dimensionalsciencehasgrowntooneofthemostimpo
6、rtant,well-controlled,andwell-developedareasoftoday'sphysicsandmathematics.Abstractmathematicsandtheoreticalphysicshaveestablishedmanybreathtakingresults,whilecondensedmatterphysicshasdevisedmanysystemsthatbehaveastwo-dimensional,someofwhichhavegreatimpactonoursociety.Ofcourse,despit
7、ethesetwo-dimensionalapplications,manyphysicistshavearguedthat`ouruniverse'couldnothavebeentwo-dimensional,thatlifecouldnothaveexistedintwodimensions,andthatthreedimensionsistheminimalfeasibledimensionalityforourworld.Inparticular,S.HawkingintalksandM.Kakuinhisbest-sellerHyperspaceha
8、vearguedthat
