Book Description
A self-contained pedagogical introduction to asymptotic safety and the functional renormalization group in quantum gravity, for graduate students and researchers.
Author : Martin Reuter
Publisher : Cambridge University Press
Page : 357 pages
File Size : 48,28 MB
Release : 2019-01-03
Category : Science
ISBN : 1107107326
A self-contained pedagogical introduction to asymptotic safety and the functional renormalization group in quantum gravity, for graduate students and researchers.
Author : Roberto Percacci
Publisher : World Scientific
Page : 313 pages
File Size : 48,59 MB
Release : 2017-02-17
Category : Science
ISBN : 9813207191
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.
Author : Herbert W. Hamber
Publisher : Springer Science & Business Media
Page : 342 pages
File Size : 37,81 MB
Release : 2008-10-20
Category : Science
ISBN : 354085293X
"Quantum Gravitation" approaches the subject from the point of view of Feynman path integrals, which provide a manifestly covariant approach in which fundamental quantum aspects of the theory such as radiative corrections and the renormalization group can be systematically and consistently addressed. It is shown that the path integral method is suitable for both perturbative as well as non-perturbative studies, and is already known to offer a framework for the theoretical investigation of non-Abelian gauge theories, the basis for three of the four known fundamental forces in nature. The book thus provides a coherent outline of the present status of the theory gravity based on Feynman’s formulation, with an emphasis on quantitative results. Topics are organized in such a way that the correspondence to similar methods and results in modern gauge theories becomes apparent. Covariant perturbation theory are developed using the full machinery of Feynman rules, gauge fixing, background methods and ghosts. The renormalization group for gravity and the existence of non-trivial ultraviolet fixed points are investigated, stressing a close correspondence with well understood statistical field theory models. The final chapter addresses contemporary issues in quantum cosmology such as scale dependent gravitational constants and quantum effects in the early universe.
Author : Steffen Gielen
Publisher : MDPI
Page : 338 pages
File Size : 44,14 MB
Release : 2020-07-01
Category : Mathematics
ISBN : 3039361783
Following the fundamental insights from quantum mechanics and general relativity, geometry itself should have a quantum description; the search for a complete understanding of this description is what drives the field of quantum gravity. Group field theory is an ambitious framework in which theories of quantum geometry are formulated, incorporating successful ideas from the fields of matrix models, ten-sor models, spin foam models and loop quantum gravity, as well as from the broader areas of quantum field theory and mathematical physics. This special issue collects recent work in group field theory and these related approaches, as well as other neighbouring fields (e.g., cosmology, quantum information and quantum foundations, statistical physics) to the extent that these are directly relevant to quantum gravity research.
Author : Daniele Oriti
Publisher : Cambridge University Press
Page : 605 pages
File Size : 40,58 MB
Release : 2009-03-05
Category : Science
ISBN : 0521860458
Containing contributions from leading researchers in this field, this book provides a complete overview of this field from the frontiers of theoretical physics research for graduate students and researchers. It introduces the most current approaches to this problem, and reviews their main achievements.
Author : Astrid Eichhorn
Publisher : Frontiers Media SA
Page : 298 pages
File Size : 17,89 MB
Release : 2021-07-15
Category : Science
ISBN : 2889710491
Author : Jácome (Jay) Armas
Publisher : Cambridge University Press
Page : 720 pages
File Size : 29,62 MB
Release : 2021-08-26
Category : Science
ISBN : 1316731871
The holy grail of theoretical physics is to find the theory of everything that combines all the forces of nature, including gravity. This book addresses the question: how far are we from such discovery? Over the last few decades, multiple roads to finding a quantum theory of gravity have been proposed but no obvious description of nature has emerged in this domain. What is to be made of this situation? This volume probes the state-of-the art in this daunting quest of theoretical physics by collecting critical interviews with nearly forty leading theorists in this field. These broad-ranging conversations give important insights and candid opinions on the various approaches to quantum gravity, including string theory, loop quantum gravity, causal set theory and asymptotic safety. This unique, readable overview provides a gateway into cutting edge research for students and others who wish to engage with the open problem of quantum gravity.
Author : Jácome Armas
Publisher : Cambridge University Press
Page : 719 pages
File Size : 49,37 MB
Release : 2021-08-26
Category : Biography & Autobiography
ISBN : 1107168872
Leading theorists share their important insights into the ongoing quest of theoretical physics to find a quantum theory of gravity.
Author : Sylvie Paycha
Publisher : American Mathematical Soc.
Page : 272 pages
File Size : 34,44 MB
Release : 2007
Category : Mathematics
ISBN : 0821840622
This volume, based on lectures and short communications at a summer school in Villa de Leyva, Colombia (July 2005), offers an introduction to some recent developments in several active topics at the interface between geometry, topology and quantum field theory. It is aimed at graduate students in physics or mathematics who might want insight in the following topics (covered in five survey lectures): Anomalies and noncommutative geometry, Deformation quantisation and Poisson algebras, Topological quantum field theory and orbifolds. These lectures are followed by nine articles on various topics at the borderline of mathematics and physics ranging from quasicrystals to invariant instantons through black holes, and involving a number of mathematical tools borrowed from geometry, algebra and analysis.
Author : Toka Diagana
Publisher : Springer
Page : 468 pages
File Size : 29,51 MB
Release : 2018-10-31
Category : Mathematics
ISBN : 3319971751
This contributed volume features invited papers on current research and applications in mathematical structures. Featuring various disciplines in the mathematical sciences and physics, articles in this volume discuss fundamental scientific and mathematical concepts as well as their applications to topical problems. Special emphasis is placed on important methods, research directions and applications of analysis within and beyond each field. Covered topics include Metric operators and generalized hermiticity, Semi-frames, Hilbert-Schmidt operator, Symplectic affine action, Fractional Brownian motion, Walker Osserman metric, Nonlinear Maxwell equations, The Yukawa model, Heisenberg observables, Nonholonomic systems, neural networks, Seiberg-Witten invariants, photon-added coherent state, electrostatic double layers, and star products and functions. All contributions are from the participants of the conference held October 2016 in Cotonou, Benin in honor of Professor Mahouton Norbert Hounkonnou for his outstanding contributions to the mathematical and physical sciences and education. Accessible to graduate students and postdoctoral researchers, this volume is a useful resource to applied scientists, applied and pure mathematicians, and mathematical and theoretical physicists.