Quantum Gravity And The Functional Renormalization Group
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Quantum Gravity and the Functional Renormalization Group by Martin Reuter,Frank Saueressig Pdf
A self-contained pedagogical introduction to asymptotic safety and the functional renormalization group in quantum gravity, for graduate students and researchers.
Asymptotically Safe Gravity by Alessia Benedetta Platania Pdf
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.
Effective Action in Quantum Gravity by I.L Buchbinder Pdf
In part one of Effective Action in Quantum Gravity, the book describes the principles of quantum field theory and the significance of and theory behind effective action. Part two deals with quantum field theory in curved space-time and the effective action. These two parts provide the tools for understanding the rest of the book, which is devoted to selected problems of quantum gravity where the effective action plays a major role. The book assumes only a basic understanding of quantum field theory and general relativity and will be of interest to postgraduate students and researchers in theoretical high-energy physics and gravitational theory.
WAVELETS AND RENORMALIZATION describes the role played by wavelets in Euclidean field theory and classical statistical mechanics. The author begins with a stream-lined introduction to quantum field theory from a rather basic point of view. Functional integrals for imaginary-time-ordered expectations are introduced early and naturally, while the connection with the statistical mechanics of classical spin systems is introduced in a later chapter.A vastly simplified (wavelet) version of the celebrated Glimm-Jaffe construction of the 3 quantum field theory is presented. It is due to Battle and Federbush, and it bases an inductively defined cluster expansion on a wavelet decomposition of the Euclidean quantum field. The presentation is reserved for the last chapter, while the more basic aspects of cluster expansions are reviewed in the chapter on classical spin systems.Wavelets themselves are studied from two different points of view arising from two disciplines. The mathematical point of view covers the basic properties of wavelets and methods for constructing well-known wavelets such as Meyer wavelets, Daubechies wavelets, etc. The physical point of view covers the renormalization group formalism, where there is a close connection between wavelets and Gaussian fixed points.The book is heavily mathematical, but avoids the theorem-proof-theorem-proof format in the interests of preserving the flow of the discussion i.e., it is written in the style of an old-fashioned theoretical physics book, but the major claims are rigorously proven. The minor themes of the book are reflection positivity, the combinatorics of cluster expansions, and the issue of phase transitions themes which have nothing to do with wavelets, but which provide necessary cultural background for the physical context."
Renormalization Group and Fixed Points by Timothy J Hollowood Pdf
This Brief presents an introduction to the theory of the renormalization group in the context of quantum field theories of relevance to particle physics. Emphasis is placed on gaining a physical understanding of the running of the couplings. The Wilsonian version of the renormalization group is related to conventional perturbative calculations with dimensional regularization and minimal subtraction. An introduction is given to some of the remarkable renormalization group properties of supersymmetric theories.
The purpose of this section is to give you a sketch of how quantum field theory works, where Feynman graphs come from and why they are so useful, where the infinities come from, and how we have learned to deal with them without compromising the physical principles involved. I am purposely treating the problem at the level of the 1940s and 1950s, so as to keep the basic ideas clear and avoid the more difficult problems and more sophisticated methods of recent years. I shall relate my discussion simply to quantum electrodynamics (QED) since that is the most familiar case and the case that was in the forefront from the beginning (though in fact I shall ignore many of the special complications that have to be dealt with when you quantize a gauge field). The methods I shall be describing are applicable to all sorts of quantized fields: the detailed factors are different but the structure of the logical development isjust the same. Not surprisingly, though, the renormalization procedure breaks down if the theory in question is nonrenormalizable. Whether nonrenormalizable theories are theories at all is a matter for debate; in any case, they hold no practical interest for physicists since they are essentially unusable. Quantum electrodynamics was devised in 1927 by Dirac, less than a year after the Schrodinger equation appeared and before the Dirac equa tion for the relativistic electron had been invented.
Progress in Group Field Theory and Related Quantum Gravity Formalisms by Steffen Gielen,Sylvain Carrozza,Daniele Oriti Pdf
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.
Course on renormalization - Functional integral, Dimensional regularization, Feynman diagrams, Renormalization, Renormalization group, Gauge symmetry, Canonical formalism, Quantum electrodynamics, Non-Abelian gauge field theories - Most modern high-energy physics, including the standard model of particle physics, is formulated by means of perturbative quantum field theory.When the perturbative expansion is performed in a naive way, it generates "divergences'', that is to say quantities that appear to be "infinite'', instead of being small. Typically, they are due to diverging improper integrals. The presence of divergences suggests that it should be possible to define the perturbative expansion in a smarter way.With the help of a cutoff, divergences become temporarily finite. Then they can be classified and moved around. Clearly, if a divergence disappears by changing the parametrization of the theory, it is not a true divergence, but just a blunder due to an unfortunate choice of variables. If there exists a reparametrization that makes all the divergences disappear, then the theory is actually convergent.Divergences can be relocated by performing all sorts of operations that in normal circumstances leave the physics unchanged, such as changes of field variables, as well as redefinitions of the parameters, in particular the coupling constants. Renormalization is the reparametrization that moves the divergences "to the right places'', assuming that such places do exist. In simple theories, fields and couplings just get multiplied by constants, whence the name re-normalization. In more complicated situations the redefinitions can even be nonpolynomial. Once the theory is renormalized, the cutoff can be safely removed, and the physical quantities become meaningful.The reparametrization solves the problem of divergences, and allows us to define the correct perturbative expansion. Under certain, rather general, assumptions it is always possible to absorb the divergences into reparametrizations. However, the price can be considerably high: the introduction of infinitely many new independent parameters. If the divergences can be cancelled by keeping the number of independent parameters finite the theory is called renormalizable. The renormalizable theories acquire a very special status among all theories.Renormalizability provides a way to select the theories. This selection is actually welcome, since it gives us a reason to discard a huge set of theories that otherwise would have to be a priori included. Among other things, no physical theory in more than four spacetime dimensions survives the selection, which makes renormalization a good candidate to explain why we live in four dimensions. The set of renormalizable theories contains the standard model in flat space. Therefore, it allows us to explain three interactions of nature out of four. Ironically, the "divergences'' are the best known quantities of quantum field theory, to the extent that certain physical amplitudes can be calculated exactly to all orders.The book contains the basic notions of renormalization. The main goals are to construct perturbative quantum field theory, study the consequences of renormalization, and show that the perturbative formulation of a wide class of quantum field theories, which includes the standard model coupled to quantum gravity, is consistent to all orders. Most issues are treated using modern techniques, privileging the most economical and powerful tools. On the contrary, not much effort is devoted to explain how such a successful theoretical framework has emerged historically. Some aspects of quantum field theory are very involved, and those who study the matter for the first time can greatly benefit from the rational, non historical approach of this book.
Coarse Graining in Quantum Gravity: Bridging the Gap between Microscopic Models and Spacetime-Physics by Astrid Eichhorn,Benjamin Bahr,Antonio D. Pereira Pdf
Mathematical Structures and Applications by Toka Diagana,Bourama Toni Pdf
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.
Introduction to Quantum Field Theory with Applications to Quantum Gravity by Iosif L. Buchbinder,Ilya Shapiro Pdf
Applications of quantum field theoretical methods to gravitational physics, both in the semiclassical and the full quantum frameworks, require a careful formulation of the fundamental basis of quantum theory, with special attention to such important issues as renormalization, quantum theory of gauge theories, and especially effective action formalism. The first part of this graduate textbook provides both a conceptual and technical introduction to the theory of quantum fields. The presentation is consistent, starting from elements of group theory, classical fields, and moving on to the effective action formalism in general gauge theories. Compared to other existing books, the general formalism of renormalization in described in more detail, and special attention paid to gauge theories. This part can serve as a textbook for a one-semester introductory course in quantum field theory. In the second part, we discuss basic aspects of quantum field theory in curved space, and perturbative quantum gravity. More than half of Part II is written with a full exposition of details, and includes elaborated examples of simplest calculations. All chapters include exercises ranging from very simple ones to those requiring small original investigations. The selection of material of the second part is done using the “must-know” principle. This means we included detailed expositions of relatively simple techniques and calculations, expecting that the interested reader will be able to learn more advanced issues independently after working through the basic material, and completing the exercises.
Approaches to Quantum Gravity by Daniele Oriti Pdf
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.
Introduction to Quantum Field Theory with Applications to Quantum Gravity by Iosif L. Buchbinder,Ilya Shapiro Pdf
This textbook presents a detailed introduction to the general concepts of quantum field theory, with special emphasis on principal aspects of functional methods and renormalization in gauge theories, and includes an introduction to semiclassical and perturbative quantum gravity in flat and curved spacetimes.