Lectures on Non-perturbative Canonical Gravity - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Lectures on Non-perturbative Canonical Gravity write by Abhay Ashtekar. This book was released on 1991. Lectures on Non-perturbative Canonical Gravity available in PDF, EPUB and Kindle. Notes prepared in Collaboration with Ranjeet S Tate It is now generally recognized that perturbative field theoretical methods that have been highly successful in the quantum description of non-gravitational interactions cannot be used as a means of constructing a quantum theory of gravity. The primary aim of the book is to present an up- to-date account of a non-perturbative, canonical quantization program for gravity. Many of the technical results obtained in the process are of interest also to differential geometry, classical general relativity and QCD. The program as a whole was highlighted in virtually every major conference in gravitational physics over the past three years.
New Perspectives in Canonical Gravity
New Perspectives in Canonical Gravity - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook New Perspectives in Canonical Gravity write by Abhay Ashtekar. This book was released on 1988. New Perspectives in Canonical Gravity available in PDF, EPUB and Kindle.
Gravity, Particles and Space-time
Gravity, Particles and Space-time - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Gravity, Particles and Space-time write by Petr Ivanovich Pronin. This book was released on 1996. Gravity, Particles and Space-time available in PDF, EPUB and Kindle. This volume comprises original and review articles on the frontier problems of the gravitation theory, theoretical and mathematical physics. The volume is dedicated to the memory of Professor Dmitri Ivanenko who made the great contribution to the physical science of the twentieth century.
Proceedings of the Summer School Geometric and Topological Methods for Quantum Field Theory
Proceedings of the Summer School Geometric and Topological Methods for Quantum Field Theory - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Proceedings of the Summer School Geometric and Topological Methods for Quantum Field Theory write by Hernan Ocampo. This book was released on 2003. Proceedings of the Summer School Geometric and Topological Methods for Quantum Field Theory available in PDF, EPUB and Kindle. This volume offers an introduction to recent developments in several active topics of research at the interface between geometry, topology and quantum field theory. These include Hopf algebras underlying renormalization schemes in quantum field theory, noncommutative geometry with applications to index theory on one hand and the study of aperiodic solids on the other, geometry and topology of low dimensional manifolds with applications to topological field theory, Chern-Simons supergravity and the anti de Sitter/conformal field theory correspondence. It comprises seven lectures organized around three main topics, noncommutative geometry, topological field theory, followed by supergravity and string theory, complemented by some short communications by young participants of the school.
Noncommutative Geometry, Quantum Fields and Motives
Noncommutative Geometry, Quantum Fields and Motives - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Noncommutative Geometry, Quantum Fields and Motives write by Alain Connes. This book was released on 2019-03-13. Noncommutative Geometry, Quantum Fields and Motives available in PDF, EPUB and Kindle. The unifying theme of this book is the interplay among noncommutative geometry, physics, and number theory. The two main objects of investigation are spaces where both the noncommutative and the motivic aspects come to play a role: space-time, where the guiding principle is the problem of developing a quantum theory of gravity, and the space of primes, where one can regard the Riemann Hypothesis as a long-standing problem motivating the development of new geometric tools. The book stresses the relevance of noncommutative geometry in dealing with these two spaces. The first part of the book deals with quantum field theory and the geometric structure of renormalization as a Riemann-Hilbert correspondence. It also presents a model of elementary particle physics based on noncommutative geometry. The main result is a complete derivation of the full Standard Model Lagrangian from a very simple mathematical input. Other topics covered in the first part of the book are a noncommutative geometry model of dimensional regularization and its role in anomaly computations, and a brief introduction to motives and their conjectural relation to quantum field theory. The second part of the book gives an interpretation of the Weil explicit formula as a trace formula and a spectral realization of the zeros of the Riemann zeta function. This is based on the noncommutative geometry of the adèle class space, which is also described as the space of commensurability classes of Q-lattices, and is dual to a noncommutative motive (endomotive) whose cyclic homology provides a general setting for spectral realizations of zeros of L-functions. The quantum statistical mechanics of the space of Q-lattices, in one and two dimensions, exhibits spontaneous symmetry breaking. In the low-temperature regime, the equilibrium states of the corresponding systems are related to points of classical moduli spaces and the symmetries to the class field theory of the field of rational numbers and of imaginary quadratic fields, as well as to the automorphisms of the field of modular functions. The book ends with a set of analogies between the noncommutative geometries underlying the mathematical formulation of the Standard Model minimally coupled to gravity and the moduli spaces of Q-lattices used in the study of the zeta function.
