LEADER 04565nam 2200637 a 450 001 9910457995303321 005 20200520144314.0 010 $a1-282-96480-1 010 $a9786612964800 010 $a1-4008-3767-7 024 7 $a10.1515/9781400837670 035 $a(CKB)2560000000049151 035 $a(EBL)664560 035 $a(OCoLC)705945735 035 $a(SSID)ssj0000469742 035 $a(PQKBManifestationID)11284090 035 $a(PQKBTitleCode)TC0000469742 035 $a(PQKBWorkID)10511176 035 $a(PQKB)10262492 035 $a(MiAaPQ)EBC664560 035 $a(DE-B1597)446583 035 $a(OCoLC)979624020 035 $a(DE-B1597)9781400837670 035 $a(Au-PeEL)EBL664560 035 $a(CaPaEBR)ebr10443134 035 $a(CaONFJC)MIL296480 035 $a(EXLCZ)992560000000049151 100 $a20080229d2008 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aGroup theory$b[electronic resource] $ebirdtracks, Lie's, and exceptional groups /$fPredrag Cvitanovic? 205 $aCourse Book 210 $aPrinceton, N.J. $cPrinceton University Press$dc2008 215 $a1 online resource (278 p.) 300 $aDescription based upon print version of record. 311 $a0-691-20298-2 311 $a0-691-11836-1 320 $aIncludes bibliographical references (p. [251]-268) and index. 327 $t Frontmatter -- $tContents -- $tAcknowledgments -- $tChapter One. Introduction -- $tChapter Two. A preview -- $tChapter Three. Invariants and reducibility -- $tChapter Four. Diagrammatic notation -- $tChapter Five. Recouplings -- $tChapter Six. Permutations -- $tChapter Seven. Casimir operators -- $tChapter Eight. Group integrals -- $tChapter Nine. Unitary groups -- $tChapter Ten. Orthogonal groups -- $tChapter Eleven. Spinors -- $tChapter Twelve. Symplectic groups -- $tChapter Thirteen. Negative dimensions -- $tChapter Fourteen. Spinors' symplectic sisters -- $tChapter Fifteen. SU(n) family of invariance groups -- $tChapter Sixteen. G2 family of invariance groups -- $tChapter Seventeen. E8 family of invariance groups -- $tChapter Eighteen. E6 family of invariance groups -- $tChapter Nineteen. F4 family of invariance groups -- $tChapter Twenty. E7 family and its negative-dimensional cousins -- $tChapter Twenty-One. Exceptional magic -- $tAppendix A. Recursive decomposition -- $tAppendix B. Properties of Young projections -- $tBibliography -- $tIndex 330 $aIf classical Lie groups preserve bilinear vector norms, what Lie groups preserve trilinear, quadrilinear, and higher order invariants? Answering this question from a fresh and original perspective, Predrag Cvitanovic takes the reader on the amazing, four-thousand-diagram journey through the theory of Lie groups. This book is the first to systematically develop, explain, and apply diagrammatic projection operators to construct all semi-simple Lie algebras, both classical and exceptional. The invariant tensors are presented in a somewhat unconventional, but in recent years widely used, "birdtracks" notation inspired by the Feynman diagrams of quantum field theory. Notably, invariant tensor diagrams replace algebraic reasoning in carrying out all group-theoretic computations. The diagrammatic approach is particularly effective in evaluating complicated coefficients and group weights, and revealing symmetries hidden by conventional algebraic or index notations. The book covers most topics needed in applications from this new perspective: permutations, Young projection operators, spinorial representations, Casimir operators, and Dynkin indices. Beyond this well-traveled territory, more exotic vistas open up, such as "negative dimensional" relations between various groups and their representations. The most intriguing result of classifying primitive invariants is the emergence of all exceptional Lie groups in a single family, and the attendant pattern of exceptional and classical Lie groups, the so-called Magic Triangle. Written in a lively and personable style, the book is aimed at researchers and graduate students in theoretical physics and mathematics. 606 $aGroup theory 608 $aElectronic books. 615 0$aGroup theory. 676 $a512/.2 686 $aSK 260$2rvk 700 $aCvitanovic?$b Predrag$046041 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910457995303321 996 $aGroup theory$92458606 997 $aUNINA