LEADER 03061cmm 2200241 a 450

001 266392

008 170322s2017 ne s 0 eng d

020 $a9789402409598 (ebook)

020 $a9789402409581 (paper)

035 $a00313350

041 0 $aeng

050 4$aQC20.7.D52

082 04$a530.15$223

090 $aE-BOOK/530.15///UE016944

100 1 $aRudolph, Gerd.$3472143

245 10$aDifferential geometry and mathematical physics.$nPart II,$pFibre bundles, topology and gauge fields$h[electronic resource] /$cby Gerd Rudolph, Matthias Schmidt.

246 30$aFibre bundles, topology and gauge fields

260 $aDordrecht :$bSpringer Netherlands :$bImprint: Springer,$c2017.

300 $axvi, 830 p. :$bill., digital ;$c24 cm.

490 1 $aTheoretical and mathematical physics,$x1864-5879

505 0 $aFibre bundles and connections -- Linear connections and Riemannian geometry -- Homotopy theory of principal fibre bundles. Classification -- Cohomology theory of fibre bundles. Characteristic classes -- Clifford algebras, spin structures and Dirac operators -- The Yang-Mills equation -- Matter fields and model building -- The gauge orbit space -- Elements of quantum gauge theory -- A Field restriction and field extension -- B The Conformal Group of the 4-sphere -- C Simple Lie algebras. Root diagrams -- D z -function regularization -- E K-theory and index bundles -- F Determinant line bundles -- G Eilenberg-MacLane spaces -- References. Index.

520 $aThe book is devoted to the study of the geometrical and topological structure of gauge theories. It consists of the following three building blocks: - Geometry and topology of fibre bundles, - Clifford algebras, spin structures and Dirac operators, - Gauge theory. Written in the style of a mathematical textbook, it combines a comprehensive presentation of the mathematical foundations with a discussion of a variety of advanced topics in gauge theory. The first building block includes a number of specific topics, like invariant connections, universal connections, H-structures and the Postnikov approximation of classifying spaces. Given the great importance of Dirac operators in gauge theory, a complete proof of the Atiyah-Singer Index Theorem is presented. The gauge theory part contains the study of Yang-Mills equations (including the theory of instantons and the classical stability analysis), the discussion of various models with matter fields (including magnetic monopoles, the Seiberg-Witten model and dimensional reduction) and the investigation of the structure of the gauge orbit space. The final chapter is devoted to elements of quantum gauge theory including the discussion of the Gribov problem, anomalies and the implementation of the non-generic gauge orbit strata in the framework of Hamiltonian lattice gauge theory. The book is addressed both to physicists and mathematicians. It is intended to be accessible to students starting from a graduate level.

650 0$aGeometry, Differential.$3139987

650 0$aMathematical physics.$3148279

650 0$aGauge fields (Physics)$3152240

650 0$aFiber bundles (Mathematics)$3148353

650 0$aTopology.$3140000

650 14$aPhysics.$3154387

650 24$aMathematical Methods in Physics.$3402935

650 24$aDifferential Geometry.$3410231

650 24$aMathematical Physics.$3402956

650 24$aAlgebraic Geometry.$3403731

650 24$aAlgebraic Topology.$3416841

650 24$aElementary Particles, Quantum Field Theory.$3402319

700 1 $aSchmidt, Matthias.$3472144

710 2 $aSpringerLink (Online service)$3374217

773 0 $tSpringer eBooks

830 0$aTheoretical and mathematical physics.$3405836

856 40$uhttps://erm.library.ntpu.edu.tw/login?url=http://dx.doi.org/10.1007/978-94-024-0959-8$z線上閱讀(Springer)

950 $aPhysics and Astronomy (Springer-11651)

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