MARC Record from marc_columbia

LEADER: 04781cam a22003974a 4500
001 6374171
005 20221122030458.0
008 070814t20082008riua b 001 0 eng
010 $a 2007060843
020 $a9780821842102 (alk. paper)
020 $a0821842102 (alk. paper)
035 $a(OCoLC)ocn165958837
035 $a(OCoLC)165958837
035 $a(NNC)6374171
035 $a6374171
040 $aDLC$cDLC$dBAKER$dBTCTA$dYDXCP$dDAY$dOrLoB-B
042 $apcc
050 00 $aQC20.7.D52$bC66 2008
082 00 $a512/.55$222
100 1 $aConnes, Alain.$0http://id.loc.gov/authorities/names/n80137982
245 10 $aNoncommutative geometry, quantum fields and motives /$cAlain Connes, Matilde Marcolli.
260 $aProvidence, R.I. :$bAmerican Mathematical Society,$c[2008], ©2008.
263 $a0712
300 $axxii, 785 pages :$billustrations ;$c26 cm.
336 $atext$btxt$2rdacontent
337 $aunmediated$bn$2rdamedia
490 1 $aColloquium publications,$x0065-9258 ;$vv. 55
500 $aPublished under license from Hindustan Book Agency--T.p. verso.
504 $aIncludes bibliographical references (p. 749-761) and index.
505 00 $gCh. 1.$tQuantum fields, noncommutative spaces, and motives -- $g1.$tIntroduction -- $g2.$tBasics of perturbative QFT -- $g3.$tFeynman diagrams -- $g4.$tDimensional regularization -- $g5.$tThe graph by graph method of Bogoliubov-Parasiuk-Hepp-Zimmermann -- $g6.$tThe Connes-Kreimer theory of perturbative renormalization -- $g7.$tRenormalization and the Riemann-Hilbert correspondence -- $g8.$tMotives in a nutshell -- $g9.$tThe Standard Model of elementary particles -- $g10.$tThe framework of (metric) noncommutative geometry -- $g11.$tThe spectral action principle -- $g12.$tNoncommutative geometry and the Standard Model -- $g13.$tThe finite noncommutative geometry -- $g14.$tThe product geometry -- $g15.$tBosons as inner fluctuations -- $g16.$tThe spectral action and the Standard Model Lagrangian -- $g17.$tThe Standard Model Lagrangian from the spectral action -- $g18.$tFunctional integral -- $g19.$tDimensional regularization and noncommutative geometry -- $gCh. 2.$tThe Riemann zeta function and noncommutative geometry -- $g1.$tIntroduction -- $g2.$tCounting primes and the zeta function -- $g3.$tClassical and quantum mechanics of zeta -- $g4.$tPrincipal values from the local trace formula -- $g5.$tQuantum states of the scaling flow -- $g6.$tThe map [actual symbol not reproducible] -- $g7.$tThe adele class space: finitely many degrees of freedom -- $g8.$tWeil's formulation of the explicit formulas -- $g9.$tSpectral realization of critical zeros of L-functions -- $g10.$tA Lefschetz formula for Archimedean local factors -- $gCh. 3.$tQuantum statistical mechanics and Galois symmetries -- $g1.$tOverview: three systems -- $g2.$tQuantum statistical mechanics -- $g3.$tQ-lattices and commensurability -- $g4.$t1-dimensional Q-lattices -- $g5.$t2-dimensional Q-lattices -- $g6.$tThe modular field -- $g7.$tArithmetic of the GL[subscript 2] system -- $g8.$tKMS states and complex multiplication -- $g9.$tQuantum statistical mechanics of Shimura varieties -- $gCh. 4.$tEndomotives, thermodynamics, and the Weil explicit formula -- $g1.$tMorphisms and categories of noncommutative spaces -- $g2.$tEndomotives -- $g3.$tMotives and noncommutative spaces: higher dimensional perspectives -- $g4.$tA thermodynamic "Frobenius" in characteristic zero -- $g5.$tA cohomological Lefschetz trace formula -- $g6.$tThe Weil proof for function fields -- $g7.$tA noncommutative geometry perspective -- $g8.$tThe analogy between QG and RH -- $g1.$tOperator algebras -- $g1.1.$tC*-algebras -- $g1.2.$tVon Neumann algebras -- $g1.3.$tThe passing of time -- $g2.$tGalois theory.
520 1 $a"The unifying theme of this book is the inter-play among noncommutative geometry, physics, and number theory. The two main objects of investigation are spaces where both the noncommutative and the motive aspects come to play a role: space-time, where the guiding principle is the problem of developing a quantum theory of gravity, and the space of primes, where one can regard the Riemann Hypothesis as a long-standing problem motivating the development of new geometric tools. The book stresses the relevance of noncommutative geometry in dealing with these two spaces."--BOOK JACKET.
650 0 $aNoncommutative differential geometry.$0http://id.loc.gov/authorities/subjects/sh97004788
650 0 $aQuantum field theory.$0http://id.loc.gov/authorities/subjects/sh85109461
700 1 $aMarcolli, Matilde.$0http://id.loc.gov/authorities/names/no00093085
830 0 $aColloquium publications (American Mathematical Society) ;$vv. 55.$0http://id.loc.gov/authorities/names/n84729842
852 00 $bmat$hQA1$i.A5225 v.55