The Decomposition of Global Conformal Invariants (AM-182)

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Publisher : Princeton University Press
ISBN 13 : 1400842727
Total Pages : 568 pages
Book Rating : 4.4/5 (8 download)

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Book Synopsis The Decomposition of Global Conformal Invariants (AM-182) by : Spyros Alexakis

Download or read book The Decomposition of Global Conformal Invariants (AM-182) written by Spyros Alexakis and published by Princeton University Press. This book was released on 2012-05-06 with total page 568 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book addresses a basic question in differential geometry that was first considered by physicists Stanley Deser and Adam Schwimmer in 1993 in their study of conformal anomalies. The question concerns conformally invariant functionals on the space of Riemannian metrics over a given manifold. These functionals act on a metric by first constructing a Riemannian scalar out of it, and then integrating this scalar over the manifold. Suppose this integral remains invariant under conformal re-scalings of the underlying metric. What information can one then deduce about the Riemannian scalar? Deser and Schwimmer asserted that the Riemannian scalar must be a linear combination of three obvious candidates, each of which clearly satisfies the required property: a local conformal invariant, a divergence of a Riemannian vector field, and the Chern-Gauss-Bonnet integrand. This book provides a proof of this conjecture. The result itself sheds light on the algebraic structure of conformal anomalies, which appear in many settings in theoretical physics. It also clarifies the geometric significance of the renormalized volume of asymptotically hyperbolic Einstein manifolds. The methods introduced here make an interesting connection between algebraic properties of local invariants--such as the classical Riemannian invariants and the more recently studied conformal invariants--and the study of global invariants, in this case conformally invariant integrals. Key tools used to establish this connection include the Fefferman-Graham ambient metric and the author's super divergence formula.

The Decomposition of Global Conformal Invariants

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Publisher : Princeton University Press
ISBN 13 : 0691153477
Total Pages : 460 pages
Book Rating : 4.6/5 (911 download)

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Book Synopsis The Decomposition of Global Conformal Invariants by : Spyros Alexakis

Download or read book The Decomposition of Global Conformal Invariants written by Spyros Alexakis and published by Princeton University Press. This book was released on 2012-05-06 with total page 460 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book addresses a basic question in differential geometry that was first considered by physicists Stanley Deser and Adam Schwimmer in 1993 in their study of conformal anomalies. The question concerns conformally invariant functionals on the space of Riemannian metrics over a given manifold. These functionals act on a metric by first constructing a Riemannian scalar out of it, and then integrating this scalar over the manifold. Suppose this integral remains invariant under conformal re-scalings of the underlying metric. What information can one then deduce about the Riemannian scalar? Deser and Schwimmer asserted that the Riemannian scalar must be a linear combination of three obvious candidates, each of which clearly satisfies the required property: a local conformal invariant, a divergence of a Riemannian vector field, and the Chern-Gauss-Bonnet integrand. This book provides a proof of this conjecture. The result itself sheds light on the algebraic structure of conformal anomalies, which appear in many settings in theoretical physics. It also clarifies the geometric significance of the renormalized volume of asymptotically hyperbolic Einstein manifolds. The methods introduced here make an interesting connection between algebraic properties of local invariants--such as the classical Riemannian invariants and the more recently studied conformal invariants--and the study of global invariants, in this case conformally invariant integrals. Key tools used to establish this connection include the Fefferman-Graham ambient metric and the author's super divergence formula.

Conformal Differential Geometry

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Publisher : Springer Science & Business Media
ISBN 13 : 3764399090
Total Pages : 161 pages
Book Rating : 4.7/5 (643 download)

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Book Synopsis Conformal Differential Geometry by : Helga Baum

Download or read book Conformal Differential Geometry written by Helga Baum and published by Springer Science & Business Media. This book was released on 2011-01-28 with total page 161 pages. Available in PDF, EPUB and Kindle. Book excerpt: Conformal invariants (conformally invariant tensors, conformally covariant differential operators, conformal holonomy groups etc.) are of central significance in differential geometry and physics. Well-known examples of such operators are the Yamabe-, the Paneitz-, the Dirac- and the twistor operator. The aim of the seminar was to present the basic ideas and some of the recent developments around Q-curvature and conformal holonomy. The part on Q-curvature discusses its origin, its relevance in geometry, spectral theory and physics. Here the influence of ideas which have their origin in the AdS/CFT-correspondence becomes visible. The part on conformal holonomy describes recent classification results, its relation to Einstein metrics and to conformal Killing spinors, and related special geometries.

Families of Conformally Covariant Differential Operators, Q-Curvature and Holography

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Publisher : Springer Science & Business Media
ISBN 13 : 3764399007
Total Pages : 490 pages
Book Rating : 4.7/5 (643 download)

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Book Synopsis Families of Conformally Covariant Differential Operators, Q-Curvature and Holography by : Andreas Juhl

Download or read book Families of Conformally Covariant Differential Operators, Q-Curvature and Holography written by Andreas Juhl and published by Springer Science & Business Media. This book was released on 2009-07-26 with total page 490 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book studies structural properties of Q-curvature from an extrinsic point of view by regarding it as a derived quantity of certain conformally covariant families of differential operators which are associated to hypersurfaces.

Fashion, Faith, and Fantasy in the New Physics of the Universe

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Publisher : Princeton University Press
ISBN 13 : 1400880289
Total Pages : 520 pages
Book Rating : 4.4/5 (8 download)

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Book Synopsis Fashion, Faith, and Fantasy in the New Physics of the Universe by : Roger Penrose

Download or read book Fashion, Faith, and Fantasy in the New Physics of the Universe written by Roger Penrose and published by Princeton University Press. This book was released on 2016-09-13 with total page 520 pages. Available in PDF, EPUB and Kindle. Book excerpt: One of the world's leading physicists questions some of the most fashionable ideas in physics today, including string theory What can fashionable ideas, blind faith, or pure fantasy possibly have to do with the scientific quest to understand the universe? Surely, theoretical physicists are immune to mere trends, dogmatic beliefs, or flights of fancy? In fact, acclaimed physicist and bestselling author Roger Penrose argues that researchers working at the extreme frontiers of physics are just as susceptible to these forces as anyone else. In this provocative book, he argues that fashion, faith, and fantasy, while sometimes productive and even essential in physics, may be leading today's researchers astray in three of the field's most important areas—string theory, quantum mechanics, and cosmology. Arguing that string theory has veered away from physical reality by positing six extra hidden dimensions, Penrose cautions that the fashionable nature of a theory can cloud our judgment of its plausibility. In the case of quantum mechanics, its stunning success in explaining the atomic universe has led to an uncritical faith that it must also apply to reasonably massive objects, and Penrose responds by suggesting possible changes in quantum theory. Turning to cosmology, he argues that most of the current fantastical ideas about the origins of the universe cannot be true, but that an even wilder reality may lie behind them. Finally, Penrose describes how fashion, faith, and fantasy have ironically also shaped his own work, from twistor theory, a possible alternative to string theory that is beginning to acquire a fashionable status, to "conformal cyclic cosmology," an idea so fantastic that it could be called "conformal crazy cosmology." The result is an important critique of some of the most significant developments in physics today from one of its most eminent figures.

Conformal Invariants

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Author :
Publisher : American Mathematical Soc.
ISBN 13 : 0821852701
Total Pages : 177 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Conformal Invariants by : Lars Valerian Ahlfors

Download or read book Conformal Invariants written by Lars Valerian Ahlfors and published by American Mathematical Soc.. This book was released on 2010-11-17 with total page 177 pages. Available in PDF, EPUB and Kindle. Book excerpt: Most conformal invariants can be described in terms of extremal properties. Conformal invariants and extremal problems are therefore intimately linked and form together the central theme of this classic book which is primarily intended for students with approximately a year's background in complex variable theory. The book emphasizes the geometric approach as well as classical and semi-classical results which Lars Ahlfors felt every student of complex analysis should know before embarking on independent research. At the time of the book's original appearance, much of this material had never appeared in book form, particularly the discussion of the theory of extremal length. Schiffer's variational method also receives special attention, and a proof of $\vert a_4\vert \leq 4$ is included which was new at the time of publication. The last two chapters give an introduction to Riemann surfaces, with topological and analytical background supplied to support a proof of the uniformization theorem. Included in this new reprint is a Foreword by Peter Duren, F. W. Gehring, and Brad Osgood, as well as an extensive errata. ... encompasses a wealth of material in a mere one hundred and fifty-one pages. Its purpose is to present an exposition of selected topics in the geometric theory of functions of one complex variable, which in the author's opinion should be known by all prospective workers in complex analysis. From a methodological point of view the approach of the book is dominated by the notion of conformal invariant and concomitantly by extremal considerations. ... It is a splendid offering. --Reviewed for Math Reviews by M. H. Heins in 1975

Spaces of PL Manifolds and Categories of Simple Maps

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Publisher :
ISBN 13 :
Total Pages : 196 pages
Book Rating : 4.:/5 (319 download)

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Book Synopsis Spaces of PL Manifolds and Categories of Simple Maps by : Friedhelm Waldhausen

Download or read book Spaces of PL Manifolds and Categories of Simple Maps written by Friedhelm Waldhausen and published by . This book was released on 1940 with total page 196 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Degenerate Diffusion Operators Arising in Population Biology

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Publisher :
ISBN 13 :
Total Pages : 324 pages
Book Rating : 4.:/5 (319 download)

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Book Synopsis Degenerate Diffusion Operators Arising in Population Biology by : Charles L. Epstein

Download or read book Degenerate Diffusion Operators Arising in Population Biology written by Charles L. Epstein and published by . This book was released on 1940 with total page 324 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Conformal Invariants, Inequalities, and Quasiconformal Maps

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Publisher : Wiley-Interscience
ISBN 13 :
Total Pages : 544 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Conformal Invariants, Inequalities, and Quasiconformal Maps by : Glen D. Anderson

Download or read book Conformal Invariants, Inequalities, and Quasiconformal Maps written by Glen D. Anderson and published by Wiley-Interscience. This book was released on 1997 with total page 544 pages. Available in PDF, EPUB and Kindle. Book excerpt: Disk contains: information on Conformal Invariants Software which accompanies the text.

Conformal Invariance and Critical Phenomena

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Publisher : Springer Science & Business Media
ISBN 13 : 3662039370
Total Pages : 433 pages
Book Rating : 4.6/5 (62 download)

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Book Synopsis Conformal Invariance and Critical Phenomena by : Malte Henkel

Download or read book Conformal Invariance and Critical Phenomena written by Malte Henkel and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 433 pages. Available in PDF, EPUB and Kindle. Book excerpt: Critical phenomena arise in a wide variety of physical systems. Classi cal examples are the liquid-vapour critical point or the paramagnetic ferromagnetic transition. Further examples include multicomponent fluids and alloys, superfluids, superconductors, polymers and fully developed tur bulence and may even extend to the quark-gluon plasma and the early uni verse as a whole. Early theoretical investigators tried to reduce the problem to a very small number of degrees of freedom, such as the van der Waals equation and mean field approximations, culminating in Landau's general theory of critical phenomena. Nowadays, it is understood that the common ground for all these phenomena lies in the presence of strong fluctuations of infinitely many coupled variables. This was made explicit first through the exact solution of the two-dimensional Ising model by Onsager. Systematic subsequent developments have been leading to the scaling theories of critical phenomena and the renormalization group which allow a precise description of the close neighborhood of the critical point, often in good agreement with experiments. In contrast to the general understanding a century ago, the presence of fluctuations on all length scales at a critical point is emphasized today. This can be briefly summarized by saying that at a critical point a system is scale invariant. In addition, conformal invaTiance permits also a non-uniform, local rescal ing, provided only that angles remain unchanged.

Conformal Invariants

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Publisher : American Mathematical Soc.
ISBN 13 : 0821869566
Total Pages : 177 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Conformal Invariants by : Lars V. Ahlfors

Download or read book Conformal Invariants written by Lars V. Ahlfors and published by American Mathematical Soc.. This book was released on with total page 177 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Conformal Invariance and Applications to Statistical Mechanics

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Publisher : World Scientific
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4./5 ( download)

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Book Synopsis Conformal Invariance and Applications to Statistical Mechanics by : Claude Itzykson

Download or read book Conformal Invariance and Applications to Statistical Mechanics written by Claude Itzykson and published by World Scientific. This book was released on 1998-09-01 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains Introductory Notes and major reprints on conformal field theory and its applications to 2-dimensional statistical mechanics of critical phenomena. The subject relates to many different areas in contemporary physics and mathematics, including string theory, integrable systems, representations of infinite Lie algebras and automorphic functions. Sample Chapter(s). Section 1: General Principles (4,851 KB). Contents: General Principles: Infinite Conformal Symmetry in Two-dimensional Quantum Field Theory (A A Belavin et al.); Conformal Invariance and Surface Critical Behaviour (J Cardy); Mathematical Background: Contravariant Form for Infinite-dimensional Lie Algebras and Superalgebras (V Kac); Verma Modules over the Virasoro Algebra (B Feigin & D Fuks); Unitary Representations of the Virasoro and Super-Virasoro Algebras (P Goddard et al.); Critical Models and Computation of Correlations: Conformal Algebra and Multipoint Correlation Functions in 2D Statistical Models (Vl Dotsenko & V Fateev); On the Identification of Finite Operator Algebras in Two-dimensional Conformally Invariant Field Theories (P Christe & R Flume); Finite Size Scaling: Conformal Invariance, the Central Charge and Universal Finite Size Amplitudes at Criticality (H BlAte et al.); Universal Term in the Free Energy at a Critical Point and the Conformal Anomaly (I Affleck); Exact Surface and Wedge Exponents for Polymers in Two Dimensions (B Duplantier & H Saleur); Modular Invariance: Modular Invariant Partition Functions in Two Dimensions (A Cappelli et al.); Modular Invariant Partition Functions for Parafermionic Field Theories (D Gepner & Z Qiu); Discrete Symmetries of Conformal Theories (J-B Zuber); Connections With Integrable Systems: Exact Exponents for Infinitely many New Multicritical Points (D Huse); Automorphic Properties of Local Height Probabilities for Integrable Solid-on-solid Models (E Date et al.); Models with c = 1: Correlation Functions on the Critical Lines of the Baxter and Ashkin-Teller Models (L Kadanoff & A Brown); Supersymmetric Critical Phenomena and the Two Dimensional Gaussian Model (D Friedan & S Shenker); Curiosities at c=1 (P Ginsparg); Coulomb Gas Picture: Lattice Derivation of Modular Invariant Partition Functions on the Torus (V Pasquier); Vicinity of the Critical Point: Integrals of Motion in Scaling 3-state Potts Model Field Theory (A Zamolodchikov); Correlation Functions and Higher Topology: The Conformal Field Theory of Orbifolds (L Dixon et al.); Conformal and Current Algebras on a General Riemann Surface (T Eguchi & H Ooguri); and other papers. Readership: Theoretical physicists in particle and statistical physics and mathematicians."

Conformal Field Theory

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Publisher : Springer Science & Business Media
ISBN 13 : 1461222567
Total Pages : 908 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis Conformal Field Theory by : Philippe Francesco

Download or read book Conformal Field Theory written by Philippe Francesco and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 908 pages. Available in PDF, EPUB and Kindle. Book excerpt: Filling an important gap in the literature, this comprehensive text develops conformal field theory from first principles. The treatment is self-contained, pedagogical, and exhaustive, and includes a great deal of background material on quantum field theory, statistical mechanics, Lie algebras and affine Lie algebras. The many exercises, with a wide spectrum of difficulty and subjects, complement and in many cases extend the text. The text is thus not only an excellent tool for classroom teaching but also for individual study. Intended primarily for graduate students and researchers in theoretical high-energy physics, mathematical physics, condensed matter theory, statistical physics, the book will also be of interest in other areas of theoretical physics and mathematics. It will prepare the reader for original research in this very active field of theoretical and mathematical physics.

Encyclopaedia of Mathematics

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Publisher : Springer Science & Business Media
ISBN 13 : 9401512795
Total Pages : 639 pages
Book Rating : 4.4/5 (15 download)

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Book Synopsis Encyclopaedia of Mathematics by : Michiel Hazewinkel

Download or read book Encyclopaedia of Mathematics written by Michiel Hazewinkel and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 639 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the second supplementary volume to Kluwer's highly acclaimed eleven-volume Encyclopaedia of Mathematics. This additional volume contains nearly 500 new entries written by experts and covers developments and topics not included in the previous volumes. These entries are arranged alphabetically throughout and a detailed index is included. This supplementary volume enhances the existing eleven volumes, and together these twelve volumes represent the most authoritative, comprehensive and up-to-date Encyclopaedia of Mathematics available.

Descent in Buildings

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Publisher : Annals of Mathematics Studies
ISBN 13 : 9780691166902
Total Pages : 0 pages
Book Rating : 4.1/5 (669 download)

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Book Synopsis Descent in Buildings by : Bernhard Matthias Mühlherr

Download or read book Descent in Buildings written by Bernhard Matthias Mühlherr and published by Annals of Mathematics Studies. This book was released on 2015 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Princeton University Press is proud to have published the Annals of Mathematics Studies since 1940. One of the oldest and most respected series in science publishing, it has included many of the most important and influential mathematical works of the twentieth century. The series continues this tradition as Princeton University Press publishes the major works of the twenty-first century. To mark the continued success of the series, all hooks are again available in paperback. For a complete list of titles, please visit the Princeton University Press website: press.princeton.edu. The most recently published volumes include: Multi-parameter Singular Integrals, by Brian Street, Hangzhou Lectures on Eigenfunctions of the Laplacian, by Christopher D. Sogge, Chow Rings, Decomposition of the Diagonal, and the Topology of Families, by Claire Voisin, Spaces of PL Manifolds and Categories of Simple Maps, by Friedhelm Waldhausen, Bjorn Jahren, and John Rognes, Degenerate Diffusion Operators Arising in Population Biology, by Charles L. Epstein and Rafe Mazzeo, The Gross-Zagier Formula on Shimura Curves, by Xinyi Yuan, Shou-wu Zhang, and Wei Zhang, Mumford-Tate Groups and Domains: Their Geometry and Arithmetic, by Mark Green, Phillip A. Griffiths, and Matt Kerr, The Decomposition of Global Conformal Invariants, by Spyros Alexakis, Some Problems of Unlikely Intersections in Arithmetic and Geometry, by Umberto Zannier, Convolution and Equidistribution: Sato-Fate Theorems for Finite-Field Mellin Transforms, by Nicholas Katz.

A Perspective on Canonical Riemannian Metrics

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Publisher : Springer Nature
ISBN 13 : 3030571858
Total Pages : 247 pages
Book Rating : 4.0/5 (35 download)

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Book Synopsis A Perspective on Canonical Riemannian Metrics by : Giovanni Catino

Download or read book A Perspective on Canonical Riemannian Metrics written by Giovanni Catino and published by Springer Nature. This book was released on 2020-10-23 with total page 247 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book focuses on a selection of special topics, with emphasis on past and present research of the authors on “canonical” Riemannian metrics on smooth manifolds. On the backdrop of the fundamental contributions given by many experts in the field, the volume offers a self-contained view of the wide class of “Curvature Conditions” and “Critical Metrics” of suitable Riemannian functionals. The authors describe the classical examples and the relevant generalizations. This monograph is the winner of the 2020 Ferran Sunyer i Balaguer Prize, a prestigious award for books of expository nature presenting the latest developments in an active area of research in mathematics.

Dissertation Abstracts International

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Publisher :
ISBN 13 :
Total Pages : 1044 pages
Book Rating : 4.F/5 ( download)

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Book Synopsis Dissertation Abstracts International by :

Download or read book Dissertation Abstracts International written by and published by . This book was released on 2007 with total page 1044 pages. Available in PDF, EPUB and Kindle. Book excerpt: