Download or read book Asymptotic Analysis of Spin Networks with Applications to Quantum Gravity written by Hal Mayi Haggard and published by . This book was released on 2011 with total page 348 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work initiates a study of the semiclassical limit of quantum gravity using a geometrical formulation of WKB theory and the Hamilton-Jacobi equation. Few conceptual principles are available to guide physicists in the construction of a quantum theory of gravity. Experimentally accessible signals are notoriously difficult to extract from existing proposals and one of the few reasonable constraints that we can impose is that the proposals agree with general relativity in the classical limit. Because general relativity is such a rich classical theory this is a non-trivial condition, one that has yet to be quantitatively achieved by any theory of quantum gravity. The main focus of the dissertation is on the semiclassics of $SU(2)$ spin networks. Spin networks play an important role in the loop gravity approach to quantum gravity, where they furnish a convenient and geometrically meaningful basis for the Hilbert space. Previous work on the semiclassics and asymptotics of spin networks have focused on a coherent state approach. Here we provide alternative methods based on geometrical Lagrangian manifolds. This new perspective is complementary; for example, calculation of amplitudes is very straightforward, and should open new research avenues. The thesis consists of two parts. In the first part, Foundations, we review the geometrical formulation of WKB theory and introduce the theory of spin networks from the beginning. These chapters make the tools and applications covered in this thesis readily accessible to new researchers and open the door to further cross-fertilization between researchers in semiclassics and loop gravity. In the second part, Applications, we focus on two applications of semiclassical theory to objects arising in loop gravity. In the loop approach to quantum gravity the geometry of space becomes discretized. Our first application is a derivation of the semiclassical spectrum and wavefunctions of the volume operator of a tetrahedral grain of space. A comparison of this spectrum with that found in loop gravity shows excellent agreement. This provides a simplified derivation of the quantization of space that strengthens earlier proposals along these lines. The second application is an asymptotic formula for the 9j-symbol including its amplitude, phase, and all of the phase adjustments. The 9j-symbol is a more complex spin network than has been treated at this level of detail before and arises as part of the vertex amplitude in spin foams, the loop gravity analog of the path integral approach to quantum gravity. More broadly this quantitative result provides further motivation for developing the asymptotics of higher 3nj-symbols; in the long term these asymptotics, which are accurate even for small quantum numbers, may furnish an effective computational tool for bridging loop gravity predictions to testable experiments.

Download or read book Semiclassical Analysis of SU 2 Spin Networks written by Liang Yu and published by . This book was released on 2010 with total page 366 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Applications of the Spin Networks and Spin Foam Models in Quantum Gravity written by and published by . This book was released on 2014 with total page 289 pages. Available in PDF, EPUB and Kindle. Book excerpt: Dotyczy: Loop quantum gravity, spin networks, spin foam, operator spin network diagrams, SL(2 C), pętlowa kwantowa grawitacja, sieci spinowe, piany spinowe, diagramy operatorowo-spin-networkowe, grupa SL(2 C).

Download or read book On Generalised Statistical Equilibrium and Discrete Quantum Gravity written by Isha Kotecha and published by Springer Nature. This book was released on 2022-01-29 with total page 180 pages. Available in PDF, EPUB and Kindle. Book excerpt: Absolute concepts of time and energy are integral to standard thermal physics, but background independent systems are devoid of them. This thesis explores the foundational question of generalising equilibrium statistical mechanics to background independent systems, and applies the resulting formulation to non-perturbative discrete quantum gravity. It offers a discussion of the rich interface of thermal physics and quantum gravity in this context, providing a broad contextualisation of such topics. This work details how standard tools from many-body physics can be generalised to discrete quantum gravity labelled with graph-based, or dual polyhedral, quanta that are common to various approaches like tensorial group field theory, loop quantum gravity, dynamical triangulations and lattice quantum gravity. It provides a systematic investigation, both conceptual and technical, of quantum gravitational Gibbs states, thermofield double vacuum states, and their application in condensate cosmology to probe questions of Big Bang singularity resolution and geometric inflation.

Download or read book Covariant Loop Quantum Gravity written by Carlo Rovelli and published by Cambridge University Press. This book was released on 2015 with total page 267 pages. Available in PDF, EPUB and Kindle. Book excerpt: A comprehensible introduction to the most fascinating research in theoretical physics: advanced quantum gravity. Ideal for researchers and graduate students.

Download or read book Quantum Gravity written by Carlo Rovelli and published by Cambridge University Press. This book was released on 2007-11-29 with total page 516 pages. Available in PDF, EPUB and Kindle. Book excerpt: Quantum gravity is perhaps the most important open problem in fundamental physics. It is the problem of merging quantum mechanics and general relativity, the two great conceptual revolutions in the physics of the twentieth century. The loop and spinfoam approach, presented in this 2004 book, is one of the leading research programs in the field. The first part of the book discusses the reformulation of the basis of classical and quantum Hamiltonian physics required by general relativity. The second part covers the basic technical research directions. Appendices include a detailed history of the subject of quantum gravity, hard-to-find mathematical material, and a discussion of some philosophical issues raised by the subject. This fascinating text is ideal for graduate students entering the field, as well as researchers already working in quantum gravity. It will also appeal to philosophers and other scholars interested in the nature of space and time.

Download or read book Quantum Gravity in 2 1 Dimensions written by Steven Carlip and published by Cambridge University Press. This book was released on 2003-12-04 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first comprehensive survey of (2+1)-dimensional quantum gravity - for graduate students and researchers.

Download or read book Computational Science and Its Applications ICCSA 2013 written by Beniamino Murgante and published by Springer. This book was released on 2013-06-22 with total page 743 pages. Available in PDF, EPUB and Kindle. Book excerpt: The five-volume set LNCS 7971-7975 constitutes the refereed proceedings of the 13th International Conference on Computational Science and Its Applications, ICCSA 2013, held in Ho Chi Minh City, Vietnam, in June 2013. Apart from the general track, ICCSA 2013 also include 33 special sessions and workshops, in various areas of computational sciences, ranging from computational science technologies, to specific areas of computational sciences, such as computer graphics and virtual reality. There are 46 papers from the general track, and 202 in special sessions and workshops.

Download or read book Symbol Correspondences for Spin Systems written by Pedro de M. Rios and published by Birkhäuser. This book was released on 2014-10-18 with total page 200 pages. Available in PDF, EPUB and Kindle. Book excerpt: In mathematical physics, the correspondence between quantum and classical mechanics is a central topic, which this book explores in more detail in the particular context of spin systems, that is, SU(2)-symmetric mechanical systems. A detailed presentation of quantum spin-j systems, with emphasis on the SO(3)-invariant decomposition of their operator algebras, is first followed by an introduction to the Poisson algebra of the classical spin system and then by a similarly detailed examination of its SO(3)-invariant decomposition. The book next proceeds with a detailed and systematic study of general quantum-classical symbol correspondences for spin-j systems and their induced twisted products of functions on the 2-sphere. This original systematic presentation culminates with the study of twisted products in the asymptotic limit of high spin numbers. In the context of spin systems it shows how classical mechanics may or may not emerge as an asymptotic limit of quantum mechanics. The book will be a valuable guide for researchers in this field and its self-contained approach also makes it a helpful resource for graduate students in mathematics and physics.

Download or read book Generating Functionals for Spin Foam Amplitudes written by Jeff Hnybida and published by . This book was released on 2014 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Various approaches to Quantum Gravity such as Loop Quantum Gravity, Spin Foam Models and Tensor-Group Field theories use invariant tensors on a group, called intertwiners, as the basic building block of transition amplitudes. For the group SU(2) the contraction of these intertwiners in the pattern of a graph produces what are called spin network amplitudes, which also have various applications and a long history. We construct a generating functional for the exact evalutation of a coherent representation of these spin network amplitudes. This generating functional is defined for arbitrary graphs and depends only on a pair of spinors for each edge. The generating functional is a meromorphic polynomial in the spinor invariants which is determined by the cycle structure of the graph. The expansion of the spin network generating function is given in terms of a newly recognized basis of SU(2) intertwiners consisting of the monomials of the holomorphic spinor invariants. This basis is labelled by the degrees of the monomials and is thus discrete. It is also overcomplete, but contains the precise amount of data to specify points in the classical space of closed polyhedra, and is in this sense coherent. We call this new basis the discrete-coherent basis. We focus our study on the 4-valent basis, which is the first non-trivial dimension, and is also the case of interest for Quantum Gravity. We find simple relations between the new basis, the orthonormal basis, and the coherent basis. The 4-simplex amplitude in the new basis depends on 20 spins and is referred to as the 20j symbol. We show that by simply summing over five of the extra spins produces the 15j symbol of the orthonormal basis. On the other hand, the 20j symbol is the exact evaluation of the coherent 4-simplex amplitude. The asymptotic limit of the 20j symbol is found to give a generalization of the Regge action to Twisted Geometry. By this we mean the five glued tetrahedra in the 4-simplex have different shapes when viewed from different frames. The imposition of the matching of shapes is known to be related to the simplicity constraints in spin foam models. Finally we discuss the process of coarse graining moves at the level of the generating functionals and give a general prescription for arbitrary graphs. A direct relation between the polynomial of cycles in the spin network generating functional and the high temperature loop expansion of the 2d Ising model is found.

Download or read book Spin Network Evaluation and the Asymptotic Behavior written by Dinush Lanka Panditharathna Jayasooriya Arachchilage and published by . This book was released on 2020 with total page 132 pages. Available in PDF, EPUB and Kindle. Book excerpt: Graphically, a spin network is a trivalent graph with weights on each edge. At any of the vertices, the sum of all three weights is even and the sum of any two weights is greater than or equal to the remaining weight. If the spin network has no free ends, then we can evaluate the spin network. Here, we propose a method to evaluate some basic spin networks using the idea of Stirling triangle. Tangent circles with integer curvatures are a natural source to make a spin network. In particular, there are spin networks corresponding the Apollonian circle packing and the Ford circle packing. We obtain the recurrence relations using the Descartes circle theorem and we evaluate the Apollonian spin network and the Ford circle spin network. We also discuss the asymptotic behavior of the Ford circle spin network.

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 Quantum Triangulations written by Mauro Carfora and published by Springer. This book was released on 2017-11-27 with total page 403 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book discusses key conceptual aspects and explores the connection between triangulated manifolds and quantum physics, using a set of case studies ranging from moduli space theory to quantum computing to provide an accessible introduction to this topic. Research on polyhedral manifolds often reveals unexpected connections between very distinct aspects of mathematics and physics. In particular, triangulated manifolds play an important role in settings such as Riemann moduli space theory, strings and quantum gravity, topological quantum field theory, condensed matter physics, critical phenomena and complex systems. Not only do they provide a natural discrete analogue to the smooth manifolds on which physical theories are typically formulated, but their appearance is also often a consequence of an underlying structure that naturally calls into play non-trivial aspects of representation theory, complex analysis and topology in a way that makes the basic geometric structures of the physical interactions involved clear. This second edition further emphasizes the essential role that triangulations play in modern mathematical physics, with a new and highly detailed chapter on the geometry of the dilatonic non-linear sigma model and its subtle and many-faceted connection with Ricci flow theory. This connection is treated in depth, pinpointing both the mathematical and physical aspects of the perturbative embedding of the Ricci flow in the renormalization group flow of non-linear sigma models. The geometry of the dilaton field is discussed from a novel standpoint by using polyhedral manifolds and Riemannian metric measure spaces, emphasizing their role in connecting non-linear sigma models’ effective action to Perelman’s energy-functional. No other published account of this matter is so detailed and informative. This new edition also features an expanded appendix on Riemannian geometry, and a rich set of new illustrations to help the reader grasp the more difficult points of the theory. The book offers a valuable guide for all mathematicians and theoretical physicists working in the field of quantum geometry and its applications.

Download or read book Spin foam Dynamics of Loop Quantum Gravity States written by and published by . This book was released on 2014 with total page 164 pages. Available in PDF, EPUB and Kindle. Book excerpt: Dotyczy: quantum cosmology, quantum gravity, Loop quantum gravity, spin networks, spin foams, kwantowa kosmologia, kwantowa grawitacja, pętlowa kwantowa grawitacja, sieci spinowe, piany spinowe.

Download or read book A First Course in Loop Quantum Gravity written by Rodolfo Gambini and published by OUP Oxford. This book was released on 2011-09-22 with total page 192 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an accessible introduction to loop quantum gravity and some of its applications, at a level suitable for undergraduate students and others with only a minimal knowledge of college level physics. In particular it is not assumed that the reader is familiar with general relativity and only minimally familiar with quantum mechanics and Hamiltonian mechanics. Most chapters end with problems that elaborate on the text, and aid learning. Applications such as loop quantum cosmology, black hole entropy and spin foams are briefly covered. The text is ideally suited for an undergraduate course in the senior year of a physics major. It can also be used to introduce undergraduates to general relativity and quantum field theory as part of a 'special topics' type of course.

Download or read book Graphs and Patterns in Mathematics and Theoretical Physics written by Mikhail Lyubich and published by American Mathematical Soc.. This book was released on 2005 with total page 443 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Stony Brook Conference, "Graphs and Patterns in Mathematics and Theoretical Physics", was dedicated to Dennis Sullivan in honor of his sixtieth birthday. The event's scientific content, which was suggested by Sullivan, was largely based on mini-courses and survey lectures. The main idea was to help researchers and graduate students in mathematics and theoretical physics who encounter graphs in their research to overcome conceptual barriers. The collection begins with Sullivan's paper, "Sigma models and string topology," which describes a background algebraic structure for the sigma model based on algebraic topology and transversality. Other contributions to the volume were organized into five sections: Feynman Diagrams, Algebraic Structures, Manifolds: Invariants and Mirror Symmetry, Combinatorial Aspects of Dynamics, and Physics. These sections, along with more research-oriented articles, contain the following surveys: "Feynman diagrams for pedestrians and mathematicians" by M. Polyak, "Notes on universal algebra" by A. Voronov, "Unimodal maps and hierarchical models" by M. Yampolsky, and "Quantum geometry in action: big bang and black holes" by A. Ashtekar. This comprehensive volume is suitable for graduate students and research mathematicians interested in graph theory and its applications in mathematics and physics.

Download or read book Computational Science and Its Applications ICCSA 2012 written by Beniamino Murgante and published by Springer. This book was released on 2012-06-16 with total page 795 pages. Available in PDF, EPUB and Kindle. Book excerpt: The four-volume set LNCS 7333-7336 constitutes the refereed proceedings of the 12th International Conference on Computational Science and Its Applications, ICCSA 2012, held in Salvador de Bahia, Brazil, in June 2012. The four volumes contain papers presented in the following workshops: 7333 - advances in high performance algorithms and applications (AHPAA); bioinspired computing and applications (BIOCA); computational geometry and applicatons (CGA); chemistry and materials sciences and technologies (CMST); cities, technologies and planning (CTP); 7334 - econometrics and multidimensional evaluation in the urban environment (EMEUE); geographical analysis, urban modeling, spatial statistics (Geo-An-Mod); 7335 - optimization techniques and applications (OTA); mobile communications (MC); mobile-computing, sensind and actuation for cyber physical systems (MSA4CPS); remote sensing (RS); 7336 - software engineering processes and applications (SEPA); software quality (SQ); security and privacy in computational sciences (SPCS); soft computing and data engineering (SCDE). The topics of the fully refereed papers are structured according to the four major conference themes: 7333 - computational methods, algorithms and scientific application; 7334 - geometric modelling, graphics and visualization; 7335 - information systems and technologies; 7336 - high performance computing and networks.