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Factorization Algebras in Quantum Field Theory: Volume 1: New Mathematical Monographs, cartea 31

Autor Kevin Costello, Owen Gwilliam
en Limba Engleză Hardback – 14 dec 2016
Factorization algebras are local-to-global objects that play a role in classical and quantum field theory which is similar to the role of sheaves in geometry: they conveniently organize complicated information. Their local structure encompasses examples like associative and vertex algebras; in these examples, their global structure encompasses Hochschild homology and conformal blocks. In this first volume, the authors develop the theory of factorization algebras in depth, but with a focus upon examples exhibiting their use in field theory, such as the recovery of a vertex algebra from a chiral conformal field theory and a quantum group from Abelian Chern-Simons theory. Expositions of the relevant background in homological algebra, sheaves and functional analysis are also included, thus making this book ideal for researchers and graduates working at the interface between mathematics and physics.
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Specificații

ISBN-13: 9781107163102
ISBN-10: 1107163102
Pagini: 398
Dimensiuni: 152 x 229 x 25 mm
Greutate: 0.75 kg
Editura: Cambridge University Press
Colecția Cambridge University Press
Seria New Mathematical Monographs

Locul publicării:New York, United States

Cuprins

1. Introduction; Part I. Prefactorization Algebras: 2. From Gaussian measures to factorization algebras; 3. Prefactorization algebras and basic examples; Part II. First Examples of Field Theories: 4. Free field theories; 5. Holomorphic field theories and vertex algebras; Part III. Factorization Algebras: 6. Factorization algebras - definitions and constructions; 7. Formal aspects of factorization algebras; 8. Factorization algebras - examples; Appendix A. Background; Appendix B. Functional analysis; Appendix C. Homological algebra in differentiable vector spaces; Appendix D. The Atiyah–Bott Lemma; References; Index.

Recenzii

'Because the subject of this book touches many advanced leading theories of quantum physics which utilize heavily mathematical machineries from a diverse range of mathematical topics, the background material needed for this book is immense. So it is very helpful and much appreciated that a 103-page four-section appendix is included in this 387-page book, to provide a very well-organized and fairly detailed review of relevant mathematical background topics, including simplicial techniques, colored operads/multicategories and their algebras, differential graded (dg) Lie algebras and their cohomology, sheaves/cosheaves, formal Hodge theory, and 'convenient, differentiable, or bornological' topological vector spaces facilitating the homological algebra for infinite-dimensional vector spaces.' Albert Sheu, Zentralblatt MATH
'It is a truth universally acknowledged that one cannot make two independent measurements at the very same place and very same time. In this book full of wit, Costello and Gwilliam show what can actually be done by taking this common lore seriously. … Reading this book requires minimal prerequisites: essentially only the basic notions of topology, of differential geometry, of homological algebra and of category theory will be needed, while all other background material … is provided in the four appendices that take up about one third of the book. Yet some familiarity with the subject is needed to really appreciate it. The reader who has even occasionally been close to the interface between algebraic topology, derived geometry and quantum field theory will enjoy many pleasant moments with Costello and Gwilliam and will find many sources of enlightenment … in their treatment of the subject.' Domenico Fiorenza, Mathematical Reviews

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Descriere

This first volume develops factorization algebras with a focus upon examples exhibiting their use in field theory, which will be useful for researchers and graduates.