Download or read book Heat Kernel Techniques and Quantum Gravity written by Stephen A. Fulling and published by Texas A & M University, Department of Mathematics. This book was released on 1995 with total page 471 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Heat Kernel and Quantum Gravity written by Ivan G. Avramidi and published by Springer Science & Business Media. This book was released on 2003-07-01 with total page 153 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book tackles quantum gravity via the so-called background field method and its effective action functional. The author presents an explicitly covariant and effective technique to calculate the de Witt coefficients and to analyze the Schwinger-de Wit asymptotic expansion of the effective action. He also investigates the ultraviolet behaviour of higher-derivative quantum gravity. The book addresses theoretical physicists, graduate students as well as researchers, but should also be of interest to physicists working in mathematical or elementary particle physics.

Download or read book Quantum Gravity Proceedings Of The Sixth Moscow Quantum Gravity Seminar written by V A Berezin and published by World Scientific. This book was released on 1998-03-09 with total page 666 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Sixth Moscow Quantum Gravity Seminar was a continuation of the series of seminars which has played an important role in the consolidation of the international quantum gravity community and which has greatly affected the development of the field. As well as papers presented at the conference, this proceedings volume includes the papers of invited speakers who were unable to attend the seminar itself.

Download or read book Heat Kernels for Elliptic and Sub elliptic Operators written by Ovidiu Calin and published by Birkhäuser. This book was released on 2010-10-22 with total page 436 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph is a unified presentation of several theories of finding explicit formulas for heat kernels for both elliptic and sub-elliptic operators. These kernels are important in the theory of parabolic operators because they describe the distribution of heat on a given manifold as well as evolution phenomena and diffusion processes. Heat Kernels for Elliptic and Sub-elliptic Operators is an ideal reference for graduate students, researchers in pure and applied mathematics, and theoretical physicists interested in understanding different ways of approaching evolution operators.

Download or read book Quantum Gravity and the Functional Renormalization Group written by Martin Reuter and published by Cambridge University Press. This book was released on 2019-01-03 with total page 357 pages. Available in PDF, EPUB and Kindle. Book excerpt: A self-contained pedagogical introduction to asymptotic safety and the functional renormalization group in quantum gravity, for graduate students and researchers.

Download or read book Heat Kernel on Lie Groups and Maximally Symmetric Spaces written by Ivan G. Avramidi and published by Springer Nature. This book was released on 2023-05-27 with total page 197 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph studies the heat kernel for the spin-tensor Laplacians on Lie groups and maximally symmetric spaces. It introduces many original ideas, methods, and tools developed by the author and provides a list of all known exact results in explicit form – and derives them – for the heat kernel on spheres and hyperbolic spaces. Part I considers the geometry of simple Lie groups and maximally symmetric spaces in detail, and Part II discusses the calculation of the heat kernel for scalar, spinor, and generic Laplacians on spheres and hyperbolic spaces in various dimensions. This text will be a valuable resource for researchers and graduate students working in various areas of mathematics – such as global analysis, spectral geometry, stochastic processes, and financial mathematics – as well in areas of mathematical and theoretical physics – including quantum field theory, quantum gravity, string theory, and statistical physics.

Download or read book Lectures on Quantum Gravity written by Andres Gomberoff and published by Springer Science & Business Media. This book was released on 2006-05-30 with total page 357 pages. Available in PDF, EPUB and Kindle. Book excerpt: The 2002 Pan-American Advanced Studies Institute School on Quantum Gravity was held at the Centro de Estudios Cientificos (CECS),Valdivia, Chile, January 4-14, 2002. The school featured lectures by ten speakers, and was attended by nearly 70 students from over 14 countries. A primary goal was to foster interaction and communication between participants from different cultures, both in the layman’s sense of the term and in terms of approaches to quantum gravity. We hope that the links formed by students and the school will persist throughout their professional lives, continuing to promote interaction and the essential exchange of ideas that drives research forward. This volume contains improved and updated versions of the lectures given at the School. It has been prepared both as a reminder for the participants, and so that these pedagogical introductions can be made available to others who were unable to attend. We expect them to serve students of all ages well.

Download or read book Coarse Graining in Quantum Gravity Bridging the Gap between Microscopic Models and Spacetime Physics written by Astrid Eichhorn and published by Frontiers Media SA. This book was released on 2021-07-15 with total page 298 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Heat Kernel Method and its Applications written by Ivan Avramidi and published by Birkhäuser. This book was released on 2015-11-26 with total page 402 pages. Available in PDF, EPUB and Kindle. Book excerpt: The heart of the book is the development of a short-time asymptotic expansion for the heat kernel. This is explained in detail and explicit examples of some advanced calculations are given. In addition some advanced methods and extensions, including path integrals, jump diffusion and others are presented. The book consists of four parts: Analysis, Geometry, Perturbations and Applications. The first part shortly reviews of some background material and gives an introduction to PDEs. The second part is devoted to a short introduction to various aspects of differential geometry that will be needed later. The third part and heart of the book presents a systematic development of effective methods for various approximation schemes for parabolic differential equations. The last part is devoted to applications in financial mathematics, in particular, stochastic differential equations. Although this book is intended for advanced undergraduate or beginning graduate students in, it should also provide a useful reference for professional physicists, applied mathematicians as well as quantitative analysts with an interest in PDEs.

Download or read book Asymptotic Formulae in Spectral Geometry written by Peter B. Gilkey and published by CRC Press. This book was released on 2003-12-17 with total page 315 pages. Available in PDF, EPUB and Kindle. Book excerpt: A great deal of progress has been made recently in the field of asymptotic formulas that arise in the theory of Dirac and Laplace type operators. Asymptotic Formulae in Spectral Geometry collects these results and computations into one book. Written by a leading pioneer in the field, it focuses on the functorial and special cases methods of computing asymptotic heat trace and heat content coefficients in the heat equation. It incorporates the work of many authors into the presentation, and includes a complete bibliography that serves as a roadmap to the literature on the subject. Geometers, mathematical physicists, and analysts alike will undoubtedly find this book to be the definitive book on the subject

Download or read book Covariant Techniques in Quantum Field Theory written by Enrique Álvarez and published by Springer Nature. This book was released on 2022-09-11 with total page 94 pages. Available in PDF, EPUB and Kindle. Book excerpt: The purpose of this book is to illustrate some of the most important techniques which are helpful in combinatorial problems when computing quantum effects in covariant theories, like general relativity. In fact, most of the techniques find application also in broader contexts, such as low energy effective (chiral) Lagrangians or even in specific problems in condensed matter. Some of the topics covered are: the background field approach and the heat kernel ideas. The arguments are explained in some detail and the presentation is meant for young researchers and advanced students who are starting working in the field. As prerequisite the reader should have attended a course in quantum field theory including Feynman’s path integral. In the Appendix a nontrivial calculation of one-loop divergences in Einstein-Hilbert gravity is explained step-by-step.

Download or read book Heat Kernel and Analysis on Manifolds written by Alexander Grigoryan and published by American Mathematical Soc.. This book was released on 2009 with total page 504 pages. Available in PDF, EPUB and Kindle. Book excerpt: The heat kernel has long been an essential tool in both classical and modern mathematics but has become especially important in geometric analysis as a result of major innovations beginning in the 1970s. The methods based on heat kernels have been used in areas as diverse as analysis, geometry, and probability, as well as in physics. This book is a comprehensive introduction to heat kernel techniques in the setting of Riemannian manifolds, which inevitably involves analysis of the Laplace-Beltrami operator and the associated heat equation. The first ten chapters cover the foundations of the subject, while later chapters deal with more advanced results involving the heat kernel in a variety of settings. The exposition starts with an elementary introduction to Riemannian geometry, proceeds with a thorough study of the spectral-theoretic, Markovian, and smoothness properties of the Laplace and heat equations on Riemannian manifolds, and concludes with Gaussian estimates of heat kernels. Grigor'yan has written this book with the student in mind, in particular by including over 400 exercises. The text will serve as a bridge between basic results and current research.Titles in this series are co-published with International Press, Cambridge, MA, USA.

Download or read book An Introduction To Covariant Quantum Gravity And Asymptotic Safety written by Roberto Percacci and published by World Scientific. This book was released on 2017-02-17 with total page 313 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book covers recent developments in the covariant formulation of quantum gravity. Developed in the 1960s by Feynman and DeWitt, by the 1980s this approach seemed to lead nowhere due to perturbative non-renormalizability. The possibility of non-perturbative renormalizability or 'asymptotic safety', originally suggested by Weinberg but largely ignored for two decades, was revived towards the end of the century by technical progress in the field of the renormalization group. It is now a very active field of research, providing an alternative to other approaches to quantum gravity.Written by one of the early contributors to this subject, this book provides a gentle introduction to the relevant ideas and calculational techniques. Several explicit calculations gradually bring the reader close to the current frontier of research. The main difficulties and present lines of development are also outlined.

Download or read book New Paths Towards Quantum Gravity written by Bernhelm Booß-Bavnbek and published by Springer. This book was released on 2010-07-23 with total page 372 pages. Available in PDF, EPUB and Kindle. Book excerpt: Aside from the obvious statement that it should be a theory capable of unifying general relativity and quantum field theory, not much is known about the true nature of quantum gravity. New ideas - and there are many of them for this is an exciting field of research - often diverge to a degree where it seems impossible to decide in which of the many possible direction(s) the ongoing developments should be further sustained. The division of the book in two (overlapping) parts reflects the duality between the physical vision and the mathematical construction. The former is represented by tutorial reviews on non-commutative geometry, on space-time discretization and renormalization and on gauge field path integrals. The latter one by lectures on cohomology, on stochastic geometry and on mathematical tools for the effective action in quantum gravity. The book will benefit everyone working or entering the field of quantum gravity research.

Download or read book Seventh Marcel Grossmann Meeting The On Recent Developments In Theoretical And Experimental General Relativity Gravitation And Relativistic Field Theories Proceedings Of The 7th Marcel Grossmann Meeting In 2 Parts written by Ruffini Remo and published by World Scientific. This book was released on 1997-03-19 with total page 2024 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since 1975, the triennial Marcel Grossmann Meetings have been organized in order to provide opportunities for discussing recent advances in gravitation, general relativity and relativisitic field theories, emphasizing mathematical foundations, physical predictions, and experimental tests.The proceedings of the Seventh Marcel Grossmann Meeting include the invited papers given at the plenary sessions, the summaries of the parallel sessions, the contributed papers presented at the parallel sessions, and the evening public lectures.The authors of these papers discuss many of the recent theoretical, observational, and experimental developments that have significant implications for the fields of physics, cosmology, and relativistic astrophysics.

Download or read book Thermal Field Theories and Their Applications written by and published by World Scientific. This book was released on 1996 with total page 474 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Thermal field theory is the study of quantum field theory at non-zero temperature. This proceedings introduces both retrospect and prospect for various aspects of thermal field theory as well as their extensive applications to condensed matter physics, high energy physics, cosmology, nuclear physics, etc. Also included are speeches memorizing the recently lamented Professor Hiroomi Umezawa, a leading physicist in thermal field theory, by his former students and colleagues."--Publisher's website.

Download or read book Asymptotically Safe Gravity written by Alessia Benedetta Platania and published by Springer. This book was released on 2018-09-20 with total page 142 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book seeks to construct a consistent fundamental quantum theory of gravity, which is often considered one of the most challenging open problems in present-day physics. It approaches this challenge using modern functional renormalization group techniques, and attempts to realize the idea of “Asymptotic Safety” originally proposed by S. Weinberg. Quite remarkably, the book makes significant progress regarding both the fundamental aspects of the program and its phenomenological consequences. The conceptual developments pioneer the construction of a well-behaved functional renormalization group equation adapted to spacetimes with a preferred time-direction. It is demonstrated that the Asymptotic Safety mechanism persists in this setting and extends to many phenomenologically interesting gravity-matter systems. These achievements constitute groundbreaking steps towards bridging the gap between quantum gravity in Euclidean and Lorentzian spacetimes.The phenomenological applications cover core topics in quantum gravity, e.g. constructing a phenomenologically viable cosmological evolution based on quantum gravity effects in the very early universe, and analyzing quantum corrections to black holes forming from a spherical collapse.As a key feature, all developments are presented in a comprehensive and accessible way. This makes the work a timely and valuable guide into the rapidly evolving field of Asymptotic Safety.