This book discusses key conceptual aspects and explores the connection between triangulated manifolds and quantum physics, using a set of case studies ranging from moduli space theory to quantum computing to provide an accessible introduction to this topic. Research on polyhedral manifolds often reveals unexpected connections between very distinct aspects of mathematics and physics. In particular, triangulated manifolds play an important role in settings such as Riemann moduli space theory, strings and quantum gravity, topological quantum field theory, condensed matter physics, critical phenomena and complex systems. Not only do they provide a natural discrete analogue to the smooth manifolds on which physical theories are typically formulated, but their appearance is also often a consequence of an underlying structure that naturally calls into play non-trivial aspects of representation theory, complex analysis and topology in a way that makes the basic geometric structures of the physical interactions involved clear. This second edition further emphasizes the essential role that triangulations play in modern mathematical physics, with a new and highly detailed chapter on the geometry of the dilatonic non-linear sigma model and its subtle and many-faceted connection with Ricci flow theory. This connection is treated in depth, pinpointing both the mathematical and physical aspects of the perturbative embedding of the Ricci flow in the renormalization group flow of non-linear sigma models. The geometry of the dilaton field is discussed from a novel standpoint by using polyhedral manifolds and Riemannian metric measure spaces, emphasizing their role in connecting non-linear sigma models’ effective action to Perelman’s energy-functional. No other published account of this matter is so detailed and informative. This new edition also features an expanded appendix on Riemannian geometry, and a rich set of new illustrations to help the reader grasp the more difficult points of the theory. The book offers a valuable guide for all mathematicians and theoretical physicists working in the field of quantum geometry and its applications.
This book contains a self-consistent treatment of a geometric averaging technique, induced by the Ricci flow, that allows comparing a given (generalized) Einstein initial data set with another distinct Einstein initial data set, both supported on a given closed n-dimensional manifold. This is a case study where two vibrant areas of research in geometric analysis, Ricci flow and Einstein constraints theory, interact in a quite remarkable way. The interaction is of great relevance for applications in relativistic cosmology, allowing a mathematically rigorous approach to the initial data set averaging problem, at least when data sets are given on a closed space-like hypersurface. The book does not assume an a priori knowledge of Ricci flow theory, and considerable space is left for introducing the necessary techniques. These introductory parts gently evolve to a detailed discussion of the more advanced results concerning a Fourier-mode expansion and a sophisticated heat kernel representation of the Ricci flow, both of which are of independent interest in Ricci flow theory. This work is intended for advanced students in mathematical physics and researchers alike.
The express purpose of these lecture notes is to go through some aspects of the simplicial quantum gravity model known as the dynamical triangula tions approach. Emphasis has been on laying the foundations of the theory and on illustrating its subtle and often unexplored connections with many distinct mathematical fields ranging from global Riemannian geometry, to moduli theory, number theory, and topology. Our exposition will concentrate on these points so that graduate students may find in these notes a useful exposition of some of the rigorous results one can -establish in this field and hopefully a source of inspiration for new exciting problems. We try as far as currently possible to expose the interplay between the analytical aspects of dynamical triangulations and the results of Monte Carlo simulations. The techniques described here are rather novel and allow us to address points of current interest in the subject of simplicial quantum gravity while requiring very little in the way of fancy field-theoretical arguments. As a consequence, these notes contain mostly original and until now unpublished material, which will hopefully be of interest both to the expert practitioner and to graduate students entering the field. Among the topics addressed here in considerable detail are the following. (i) An analytical discussion of the geometry of dynamical triangulations in dimensions n == 3 and n == 4.
Research on polyhedral manifolds often points to unexpected connections between very distinct aspects of Mathematics and Physics. In particular triangulated manifolds play quite a distinguished role in such settings as Riemann moduli space theory, strings and quantum gravity, topological quantum field theory, condensed matter physics, and critical phenomena. Not only do they provide a natural discrete analogue to the smooth manifolds on which physical theories are typically formulated, but their appearance is rather often a consequence of an underlying structure which naturally calls into play non-trivial aspects of representation theory, of complex analysis and topology in a way which makes manifest the basic geometric structures of the physical interactions involved. Yet, in most of the existing literature, triangulated manifolds are still merely viewed as a convenient discretization of a given physical theory to make it more amenable for numerical treatment. The motivation for these lectures notes is thus to provide an approachable introduction to this topic, emphasizing the conceptual aspects, and probing, through a set of cases studies, the connection between triangulated manifolds and quantum physics to the deepest. This volume addresses applied mathematicians and theoretical physicists working in the field of quantum geometry and its applications.
Research on polyhedral manifolds often points to unexpected connections between very distinct aspects of Mathematics and Physics. In particular triangulated manifolds play quite a distinguished role in such settings as Riemann moduli space theory, strings and quantum gravity, topological quantum field theory, condensed matter physics, and critical phenomena. Not only do they provide a natural discrete analogue to the smooth manifolds on which physical theories are typically formulated, but their appearance is rather often a consequence of an underlying structure which naturally calls into play non-trivial aspects of representation theory, of complex analysis and topology in a way which makes manifest the basic geometric structures of the physical interactions involved. Yet, in most of the existing literature, triangulated manifolds are still merely viewed as a convenient discretization of a given physical theory to make it more amenable for numerical treatment. The motivation for these lectures notes is thus to provide an approachable introduction to this topic, emphasizing the conceptual aspects, and probing, through a set of cases studies, the connection between triangulated manifolds and quantum physics to the deepest. This volume addresses applied mathematicians and theoretical physicists working in the field of quantum geometry and its applications.
This book contains a self-consistent treatment of a geometric averaging technique, induced by the Ricci flow, that allows comparing a given (generalized) Einstein initial data set with another distinct Einstein initial data set, both supported on a given closed n-dimensional manifold. This is a case study where two vibrant areas of research in geometric analysis, Ricci flow and Einstein constraints theory, interact in a quite remarkable way. The interaction is of great relevance for applications in relativistic cosmology, allowing a mathematically rigorous approach to the initial data set averaging problem, at least when data sets are given on a closed space-like hypersurface. The book does not assume an a priori knowledge of Ricci flow theory, and considerable space is left for introducing the necessary techniques. These introductory parts gently evolve to a detailed discussion of the more advanced results concerning a Fourier-mode expansion and a sophisticated heat kernel representation of the Ricci flow, both of which are of independent interest in Ricci flow theory. This work is intended for advanced students in mathematical physics and researchers alike.
The express purpose of these lecture notes is to go through some aspects of the simplicial quantum gravity model known as the dynamical triangula tions approach. Emphasis has been on laying the foundations of the theory and on illustrating its subtle and often unexplored connections with many distinct mathematical fields ranging from global Riemannian geometry, to moduli theory, number theory, and topology. Our exposition will concentrate on these points so that graduate students may find in these notes a useful exposition of some of the rigorous results one can -establish in this field and hopefully a source of inspiration for new exciting problems. We try as far as currently possible to expose the interplay between the analytical aspects of dynamical triangulations and the results of Monte Carlo simulations. The techniques described here are rather novel and allow us to address points of current interest in the subject of simplicial quantum gravity while requiring very little in the way of fancy field-theoretical arguments. As a consequence, these notes contain mostly original and until now unpublished material, which will hopefully be of interest both to the expert practitioner and to graduate students entering the field. Among the topics addressed here in considerable detail are the following. (i) An analytical discussion of the geometry of dynamical triangulations in dimensions n == 3 and n == 4.
Temos o prazer de lançar o primeiro livro internacional do ano de 2022 voltado a área do desenvolvimento, que tem como título Principles and concepts for development in nowadays society, essa obra contém 152 artigos voltados a área multidisciplinar, sendo a mesma pela Seven Publicações Ltda. A Seven Editora, agradece e enaltasse os autores que fizeram parte desse livro. Desejamos uma boa leitura a todos
Mauro Javier Cárdenas, the critically-acclaimed author of The Revolutionaries Try Again—“an original, insubordinate novel” (New York Times)—pens a profound story of literature about a man coming to terms with his dysfunctional Colombian family, as well as his own behavior, as an immigrant in America. Antonio wants to avoid thinking about his sister—even though he knows he won’t be able to avoid thinking about his sister—because his sister is on the run after allegedly threatening to shoot her neighbors, and has been claiming that Antonio, Obama, the Pentagon, and their mother are all conspiring against her. Nevertheless, Antonio is going to try his best to be as avoidant as possible, because he worries that what’s been happening to his sister might somehow infect his relatively contented, ordered American life, and destabilize the precarious arrangement with his ex-wife that’s allowed him to stay close to his two daughters. In fact, he’s busy doing everything except facing his problems head-on: transcribing recordings of his mother speaking about their troubled life in Colombia, transcribing recordings of his ex-wife speaking about her idyllic life in the Czech Republic; writing about former girlfriends whose words and deeds still recur in his mind; rereading stories by American writers that allow him to skirt the subject of his sister’s state of mind without completely destroying his own. Written in long, unravelling sentences that accommodate all the detritus of thought—scenes real and imagined, headphones and heartache, Toblerones and Thomas Bernhard—Aphasia captures the immensity of the present moment as well as the pain of the past. It cements Mauro Javier Cárdenas’s place as one of the most innovative and extraordinary novelists working today.
Fifty years after its first publication, the multimillion-copy international bestseller is available again in English, sharing the heartbreaking tale of a gifted, mischievous, direly misunderstood boy growing up in Rio de Janeiro. When Zezé grows up, he wants to be a poet in a bow tie. For now the precocious young boy entertains himself by playing clever pranks on the residents of his Rio de Janeiro neighborhood, stunts for which his parents and siblings punish him severely. Lately, with his father out of work, the beatings have become harsher. Zezé’s only solace comes from his time at school, his hours secretly spent singing with a street musician, and the refuge he finds with his precious magical orange tree. When Zezé finally makes a real friend, his life begins to change, opening him up to human tenderness but also wrenching sorrow. Never out of print in Brazil since it was first published in 1968, My Sweet Orange Tree, inspired by the author’s own childhood, has been translated into many languages and has won the hearts of millions of young readers across the globe.
Two friends are drawn into a mystery of love and murder from a past they cannot know; a boy clumsily carries a broken heart through a day of parades; a woman exacts a daily revenge for a suspected crime from a husband long since gone; and love gleefully appears out of nowhere on a wet afternoon, on Gay Street. Gay Street. In these fourteen stories, a Northern writer documents, teases and exalts the lives walking or pausing on this Southern, and very real, avenue in Knoxville, Tennessee.
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