A mathematical introduction to conformal field theory /
Schottenloher, Martin, 1944-
A mathematical introduction to conformal field theory / M. Schottenloher. - Second edition - 1 online resource (xv, 249 pages) : illustrations - - Lecture notes in physics ; 759 . - Lecture notes in physics ; 759. .
Includes bibliographical references and index.
Mathematical 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.
The 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.
English.
9783540686286 3540686282 9783540686255 3540686258 9788354068624 8354068625
10.1007/978-3-540-68628-6 doi (WaSeSS)ssj0000318811
978-3-540-68625-5 Springer http://www.springerlink.com
Quantum field theory.
Conformal invariants.
Théorie quantique des champs.
Invariants conformes.
Physique.
Conformal invariants
Quantum field theory
QC174.52.C66 / S36 2008eb
530.143
A mathematical introduction to conformal field theory / M. Schottenloher. - Second edition - 1 online resource (xv, 249 pages) : illustrations - - Lecture notes in physics ; 759 . - Lecture notes in physics ; 759. .
Includes bibliographical references and index.
Mathematical 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.
The 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.
English.
9783540686286 3540686282 9783540686255 3540686258 9788354068624 8354068625
10.1007/978-3-540-68628-6 doi (WaSeSS)ssj0000318811
978-3-540-68625-5 Springer http://www.springerlink.com
Quantum field theory.
Conformal invariants.
Théorie quantique des champs.
Invariants conformes.
Physique.
Conformal invariants
Quantum field theory
QC174.52.C66 / S36 2008eb
530.143