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020 _a9783540686286
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024 7 _a10.1007/978-3-540-68628-6
_2doi
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072 7 _aPHU
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072 7 _aSCI040000
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082 0 4 _a530.15
_223
100 1 _aSchottenloher, M.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
245 1 2 _aA Mathematical Introduction to Conformal Field Theory
_h[electronic resource] /
_cby M. Schottenloher.
250 _a2.
264 1 _aBerlin, Heidelberg :
_bSpringer Berlin Heidelberg,
_c2008.
300 _aXV, 249 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 ;
_v759
505 0 _aMathematical Preliminaries -- Conformal Transformations and Conformal Killing Fields -- The Conformal Group -- Central Extensions of Groups -- Central Extensions of Lie Algebras and Bargmann’s Theorem -- The Virasoro Algebra -- First Steps Toward Conformal Field Theory -- Representation Theory of the Virasoro Algebra -- String Theory as a Conformal Field Theory -- Axioms of Relativistic Quantum Field Theory -- Foundations of Two-Dimensional Conformal Quantum Field Theory -- Vertex Algebras -- Mathematical Aspects of the Verlinde Formula -- Appendix A.
520 _aThe first part of this book gives a detailed, self-contained and mathematically rigorous exposition of classical conformal symmetry in n dimensions and its quantization in two dimensions. In particular, the conformal groups are determined and the appearance of the Virasoro algebra in the context of the quantization of two-dimensional conformal symmetry is explained via the classification of central extensions of Lie algebras and groups. The second part surveys some more advanced topics of conformal field theory, such as the representation theory of the Virasoro algebra, conformal symmetry within string theory, an axiomatic approach to Euclidean conformally covariant quantum field theory and a mathematical interpretation of the Verlinde formula in the context of moduli spaces of holomorphic vector bundles on a Riemann surface. The substantially revised and enlarged second edition makes in particular the second part of the book more self-contained and tutorial, with many more examples given. Furthermore, two new chapters on Wightman's axioms for quantum field theory and vertex algebras broaden the survey of advanced topics. An outlook making the connection with most recent developments has also been added.
650 0 _aMathematical physics.
650 0 _aGlobal analysis.
650 0 _aQuantum theory.
650 0 _aAlgebra.
650 1 4 _aMathematical Methods in Physics.
_0http://scigraph.springernature.com/things/product-market-codes/P19013
650 2 4 _aGlobal Analysis and Analysis on Manifolds.
_0http://scigraph.springernature.com/things/product-market-codes/M12082
650 2 4 _aElementary Particles, Quantum Field Theory.
_0http://scigraph.springernature.com/things/product-market-codes/P23029
650 2 4 _aAlgebra.
_0http://scigraph.springernature.com/things/product-market-codes/M11000
650 2 4 _aQuantum Field Theories, String Theory.
_0http://scigraph.springernature.com/things/product-market-codes/P19048
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9783642088155
776 0 8 _iPrinted edition:
_z9783540864318
776 0 8 _iPrinted edition:
_z9783540686255
830 0 _aLecture Notes in Physics,
_x0075-8450 ;
_v759
856 4 0 _uhttps://doi.org/10.1007/978-3-540-68628-6
912 _aZDB-2-PHA
912 _aZDB-2-LNP
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