The Decomposition Of Global Conformal Invariants
DOWNLOAD
Download The Decomposition Of Global Conformal Invariants PDF/ePub or read online books in Mobi eBooks. Click Download or Read Online button to get The Decomposition Of Global Conformal Invariants book now. This website allows unlimited access to, at the time of writing, more than 1.5 million titles, including hundreds of thousands of titles in various foreign languages. If the content not found or just blank you must refresh this page
The Decomposition Of Global Conformal Invariants Am 182
DOWNLOAD
Author : Spyros Alexakis
language : en
Publisher: Princeton University Press
Release Date : 2012-05-06
The Decomposition Of Global Conformal Invariants Am 182 written by Spyros Alexakis and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-05-06 with Mathematics categories.
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
DOWNLOAD
Author : Spyros Alexakis
language : en
Publisher: Princeton University Press
Release Date : 2012-05-06
The Decomposition Of Global Conformal Invariants written by Spyros Alexakis and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-05-06 with Mathematics categories.
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
DOWNLOAD
Author : Helga Baum
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-01-28
Conformal Differential Geometry written by Helga Baum and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-01-28 with Mathematics categories.
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
DOWNLOAD
Author : Andreas Juhl
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-07-26
Families Of Conformally Covariant Differential Operators Q Curvature And Holography written by Andreas Juhl and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-07-26 with Mathematics categories.
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.
Conformal Invariants
DOWNLOAD
Author : Lars Valerian Ahlfors
language : en
Publisher: American Mathematical Soc.
Release Date : 2010-11-17
Conformal Invariants written by Lars Valerian Ahlfors and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-11-17 with Mathematics categories.
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
Fashion Faith And Fantasy In The New Physics Of The Universe
DOWNLOAD
Author : Roger Penrose
language : en
Publisher: Princeton University Press
Release Date : 2016-09-13
Fashion Faith And Fantasy In The New Physics Of The Universe written by Roger Penrose and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-09-13 with Science categories.
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 Invariance And Critical Phenomena
DOWNLOAD
Author : Malte Henkel
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-14
Conformal Invariance And Critical Phenomena written by Malte Henkel and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-14 with Science categories.
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.
Conformally Invariant Processes In The Plane
DOWNLOAD
Author : Gregory F. Lawler
language : en
Publisher: American Mathematical Soc.
Release Date : 2008
Conformally Invariant Processes In The Plane written by Gregory F. Lawler and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Mathematics categories.
Presents an introduction to the conformally invariant processes that appear as scaling limits. This book covers such topics as stochastic integration, and complex Brownian motion and measures derived from Brownian motion. It is suitable for those interested in random processes and their applications in theoretical physics.
Conformal Invariants
DOWNLOAD
Author : Lars V. Ahlfors
language : en
Publisher: American Mathematical Soc.
Release Date :
Conformal Invariants written by Lars V. Ahlfors and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on with categories.
Conformal Invariants Inequalities And Quasiconformal Maps
DOWNLOAD
Author : Glen D. Anderson
language : en
Publisher: Wiley-Interscience
Release Date : 1997
Conformal Invariants Inequalities And Quasiconformal Maps written by Glen D. Anderson and has been published by Wiley-Interscience this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997 with Mathematics categories.
Disk contains: information on Conformal Invariants Software which accompanies the text.