Heat Kernel Techniques and Quantum Gravity
Author: Stephen A. Fulling
Publisher: Texas A & M University, Department of Mathematics
Published: 1995
Total Pages: 471
ISBN-13: 9780963072832
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Heat Kernel and Quantum Gravity
Author: Ivan G. Avramidi
Publisher: Springer Science & Business Media
Published: 2003-07-01
Total Pages: 153
ISBN-13: 3540465235
DOWNLOAD EBOOK →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.
Quantum Gravity: Proceedings Of The Sixth Moscow Quantum Gravity Seminar
Author: V A Berezin
Publisher: World Scientific
Published: 1998-03-09
Total Pages: 666
ISBN-13: 9814546305
DOWNLOAD EBOOK →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.
Heat Kernel on Lie Groups and Maximally Symmetric Spaces
Author: Ivan G. Avramidi
Publisher: Springer Nature
Published: 2023-05-27
Total Pages: 197
ISBN-13: 3031274512
DOWNLOAD EBOOK →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.
Heat Kernels for Elliptic and Sub-elliptic Operators
Author: Ovidiu Calin
Publisher: Birkhäuser
Published: 2010-10-22
Total Pages: 436
ISBN-13: 9780817649944
DOWNLOAD EBOOK →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.
Quantum Gravity and the Functional Renormalization Group
Author: Martin Reuter
Publisher: Cambridge University Press
Published: 2019-01-03
Total Pages: 357
ISBN-13: 1107107326
DOWNLOAD EBOOK →A self-contained pedagogical introduction to asymptotic safety and the functional renormalization group in quantum gravity, for graduate students and researchers.
Lectures on Quantum Gravity
Author: Andres Gomberoff
Publisher: Springer Science & Business Media
Published: 2006-05-30
Total Pages: 357
ISBN-13: 0387249923
DOWNLOAD EBOOK →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.
Coarse Graining in Quantum Gravity: Bridging the Gap between Microscopic Models and Spacetime-Physics
Author: Astrid Eichhorn
Publisher: Frontiers Media SA
Published: 2021-07-15
Total Pages: 298
ISBN-13: 2889710491
DOWNLOAD EBOOK →Heat Kernel Method and its Applications
Author: Ivan Avramidi
Publisher: Birkhäuser
Published: 2015-11-26
Total Pages: 402
ISBN-13: 3319262661
DOWNLOAD EBOOK →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.
Asymptotic Formulae in Spectral Geometry
Author: Peter B. Gilkey
Publisher: CRC Press
Published: 2003-12-17
Total Pages: 315
ISBN-13: 1135440743
DOWNLOAD EBOOK →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
