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020 _a9783540315223
_9978-3-540-31522-3
024 7 _a10.1007/b104936
_2doi
050 4 _aQC5.53
072 7 _aPHU
_2bicssc
072 7 _aSCI040000
_2bisacsh
072 7 _aPHU
_2thema
082 0 4 _a530.15
_223
245 1 0 _aGeometric and Topological Methods for Quantum Field Theory
_h[electronic resource] /
_cedited by Hernán Ocampo, Sylvie Paycha, Andrés Vargas.
264 1 _aBerlin, Heidelberg :
_bSpringer Berlin Heidelberg,
_c2005.
300 _aXV, 230 p.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aLecture Notes in Physics,
_x0075-8450 ;
_v668
505 0 _aKnot Invariants and Configuration Space Integrals (Christine Lescop) -- Euclidean Quantum Field Theory on Commutative and Noncommutative Spaces (Raimar Wulkenhaar) -- Introduction to String Compactification (Anamaria Font, Stefan Theisen) -- Index Theorems and Noncommutative Topology (Thierry Fack).
520 _aThis volume offers an introduction, in the form of four extensive lectures, to some recent developments in several active topics at the interface between geometry, topology and quantum field theory. The first lecture is by Christine Lescop on knot invariants and configuration spaces, in which a universal finite-type invariant for knots is constructed as a series of integrals over configuration spaces. This is followed by the contribution of Raimar Wulkenhaar on Euclidean quantum field theory from a statistical point of view. The author also discusses possible renormalization techniques on noncommutative spaces. The third lecture is by Anamaria Font and Stefan Theisen on string compactification with unbroken supersymmetry. The authors show that this requirement leads to internal spaces of special holonomy and describe Calabi-Yau manifolds in detail. The last lecture, by Thierry Fack, is devoted to a K-theory proof of the Atiyah-Singer index theorem and discusses some applications of K-theory to noncommutative geometry. These lectures notes, which are aimed in particular at graduate students in physics and mathematics, start with introductory material before presenting more advanced results. Each chapter is self-contained and can be read independently.
650 0 _aMathematical physics.
650 0 _aQuantum theory.
650 0 _aCell aggregation
_xMathematics.
650 0 _aGlobal differential geometry.
650 1 4 _aMathematical Methods in Physics.
_0http://scigraph.springernature.com/things/product-market-codes/P19013
650 2 4 _aQuantum Field Theories, String Theory.
_0http://scigraph.springernature.com/things/product-market-codes/P19048
650 2 4 _aElementary Particles, Quantum Field Theory.
_0http://scigraph.springernature.com/things/product-market-codes/P23029
650 2 4 _aManifolds and Cell Complexes (incl. Diff.Topology).
_0http://scigraph.springernature.com/things/product-market-codes/M28027
650 2 4 _aDifferential Geometry.
_0http://scigraph.springernature.com/things/product-market-codes/M21022
700 1 _aOcampo, Hernán.
_eeditor.
_4edt
_4http://id.loc.gov/vocabulary/relators/edt
700 1 _aPaycha, Sylvie.
_eeditor.
_4edt
_4http://id.loc.gov/vocabulary/relators/edt
700 1 _aVargas, Andrés.
_eeditor.
_4edt
_4http://id.loc.gov/vocabulary/relators/edt
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783642063510
776 0 8 _iPrinted edition:
_z9783540806677
776 0 8 _iPrinted edition:
_z9783540242833
830 0 _aLecture Notes in Physics,
_x0075-8450 ;
_v668
856 4 0 _uhttps://doi.org/10.1007/b104936
912 _aZDB-2-PHA
912 _aZDB-2-LNP
999 _c9578
_d9578