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1 Carfora, Mauro Quantum Triangulations I09664 2017 eBook  
2 Platania, Alessia Benedetta Asymptotically Safe Gravity I08869 2018 eBook  
3 Marmo, G Classical and Quantum Physics I08690 2019 eBook  
4 Blanchard, Philipp Random Walks and Diffusions on Graphs and Databases I07722 2011 eBook  
5 B??r, Christian Quantum Field Theory on Curved Spacetimes I07207 2009 eBook  
6 Ocampo, Hernan Geometric and Topological Methods for Quantum Field Theory I07121 2005 eBook  
7 Carfora, Mauro Quantum Triangulations I06607 2012 eBook  
8 Frauendiener, J??rg Analytical and Numerical Approaches to Mathematical Relativity I06140 2006 eBook  
9 Borchers, Hans J??rgen Mathematical Implications of Einstein-Weyl Causality I05419 2006 eBook  
10 Breitenlohner, Peter Renormalization of Quantum Field Theories with Non-linear Field Transformations I05096 1988 eBook  
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TitleQuantum Triangulations : Moduli Space, Quantum Computing, Non-Linear Sigma Models and Ricci Flow
Author(s)Carfora, Mauro;Marzuoli, Annalisa
PublicationCham, 1. Imprint: Springer 2. Springer International Publishing, 2017.
DescriptionXX, 392 p. 113 illus., 92 illus. in color : online resource
Abstract NoteThis 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
ISBN,Price9783319679372
Keyword(s)1. Classical and Quantum Gravitation, Relativity Theory 2. COMPLEX MANIFOLDS 3. EBOOK 4. EBOOK - SPRINGER 5. GRAVITATION 6. Manifolds (Mathematics) 7. Manifolds and Cell Complexes (incl. Diff.Topology) 8. Mathematical Applications in the Physical Sciences 9. MATHEMATICAL PHYSICS 10. Numerical and Computational Physics, Simulation 11. PHYSICS 12. QUANTUM PHYSICS
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TitleAsymptotically Safe Gravity : From Spacetime Foliation to Cosmology
Author(s)Platania, Alessia Benedetta
PublicationCham, 1. Imprint: Springer 2. Springer International Publishing, 2018.
DescriptionXV, 142 p. 87 illus., 13 illus. in color : online resource
Abstract NoteThis 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
ISBN,Price9783319987941
Keyword(s)1. Classical and Quantum Gravitation, Relativity Theory 2. COMPLEX MANIFOLDS 3. COSMOLOGY 4. EBOOK 5. EBOOK - SPRINGER 6. GRAVITATION 7. Manifolds (Mathematics) 8. Manifolds and Cell Complexes (incl. Diff.Topology)
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3.     
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TitleClassical and Quantum Physics : 60 Years Alberto Ibort Fest Geometry, Dynamics, and Control
Author(s)Marmo, G;Mart??n de Diego, David;Mu??oz Lecanda, Miguel
PublicationCham, 1. Imprint: Springer 2. Springer International Publishing, 2019.
DescriptionXXVI, 374 p. 46 illus., 14 illus. in color : online resource
Abstract NoteThis proceedings is based on the interdisciplinary workshop held in Madrid, 5-9 March 2018, dedicated to Alberto Ibort on his 60th birthday. Alberto has great and significantly contributed to many fields of mathematics and physics, always with highly original and innovative ideas. Most of Albertos???s scientific activity has been motivated by geometric ideas, concepts and tools that are deeply related to the framework of classical dynamics and quantum mechanics. Let us mention some of the fields of expertise of Alberto Ibort: Geometric Mechanics; Constrained Systems; Variational Principles; Multisymplectic structures for field theories; Super manifolds; Inverse problem for Bosonic and Fermionic systems; Quantum Groups, Integrable systems, BRST Symmetries; Implicit differential equations; Yang-Mills Theories; BiHamiltonian Systems; Topology Change and Quantum Boundary Conditions; Classical and Quantum Control; Orthogonal Polynomials; Quantum Field Theory and Noncommutative Spaces; Classical and Quantum Tomography; Quantum Mechanics on phase space; Wigner-Weyl formalism; Lie-Jordan Algebras, Classical and Quantum; Quantum-to-Classical transition; Contraction of Associative Algebras; contact geometry, among many others. In each contribution, one may find not only technical novelties but also completely new way of looking at the considered problems. Even an experienced reader, reading Alberto's contributions on his field of expertise, will find new perspectives on the considered topic. His enthusiasm is happily contagious, for this reason he has had, and still has, very bright students wishing to elaborate their PhD thesis under his guidance.What is more impressive, is the broad list of rather different topics on which he has contributed
ISBN,Price9783030247485
Keyword(s)1. Associative rings 2. Associative Rings and Algebras 3. CALCULUS OF VARIATIONS 4. Calculus of Variations and Optimal Control; Optimization 5. COMPLEX MANIFOLDS 6. DIFFERENTIAL GEOMETRY 7. EBOOK 8. EBOOK - SPRINGER 9. Manifolds (Mathematics) 10. Manifolds and Cell Complexes (incl. Diff.Topology) 11. MATHEMATICAL PHYSICS 12. Rings (Algebra) 13. Theoretical, Mathematical and Computational Physics
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TitleRandom Walks and Diffusions on Graphs and Databases : An Introduction
Author(s)Blanchard, Philipp;Volchenkov, Dimitri
PublicationBerlin, Heidelberg, 1. Imprint: Springer 2. Springer Berlin Heidelberg, 2011.
DescriptionXIV, 262 p : online resource
Abstract NoteMost networks and databases that humans have to deal with contain large, albeit finite number of units. Their structure, for maintaining functional consistency of the components, is essentially not random and calls for a precise quantitative description of relations between nodes (or data units) and all network components. This book is an introduction, for both graduate students and newcomers to the field, to the theory of graphs and random walks on such graphs. The methods based on random walks and diffusions for exploring the structure of finite connected graphs and databases are reviewed (Markov chain analysis). This provides the necessary basis for consistently discussing a number of applications such diverse as electric resistance networks, estimation of land prices, urban planning, linguistic databases, music, and gene expression regulatory networks
ISBN,Price9783642195921
Keyword(s)1. Applications of Graph Theory and Complex Networks 2. COMPLEX MANIFOLDS 3. COMPLEXITY 4. COMPUTATIONAL COMPLEXITY 5. Data structures (Computer science) 6. Data Structures and Information Theory 7. EBOOK 8. EBOOK - SPRINGER 9. Manifolds (Mathematics) 10. Manifolds and Cell Complexes (incl. Diff.Topology) 11. PHYSICS
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TitleQuantum Field Theory on Curved Spacetimes : Concepts and Mathematical Foundations
Author(s)B??r, Christian;Fredenhagen, Klaus
PublicationBerlin, Heidelberg, 1. Imprint: Springer 2. Springer Berlin Heidelberg, 2009.
DescriptionX, 160 p. 30 illus : online resource
Abstract NoteAfter some decades of work a satisfactory theory of quantum gravity is still not available; moreover, there are indications that the original field theoretical approach may be better suited than originally expected. There, to first approximation, one is left with the problem of quantum field theory on Lorentzian manifolds. Surprisingly, this seemingly modest approach leads to far reaching conceptual and mathematical problems and to spectacular predictions, the most famous one being the Hawking radiation of black holes. Ingredients of this approach are the formulation of quantum physics in terms of C*-algebras, the geometry of Lorentzian manifolds, in particular their causal structure, and linear hyperbolic differential equations where the well-posedness of the Cauchy problem plays a distinguished role, as well as more recently the insights from suitable concepts such as microlocal analysis. This primer is an outgrowth of a compact course given by the editors and contributing authors to an audience of advanced graduate students and young researchers in the field, and assumes working knowledge of differential geometry and functional analysis on the part of the reader
ISBN,Price9783642027802
Keyword(s)1. Classical and Quantum Gravitation, Relativity Theory 2. COMPLEX MANIFOLDS 3. EBOOK 4. EBOOK - SPRINGER 5. Elementary particles (Physics) 6. Elementary Particles, Quantum Field Theory 7. GRAVITATION 8. Manifolds (Mathematics) 9. Manifolds and Cell Complexes (incl. Diff.Topology) 10. Mathematical Methods in Physics 11. PHYSICS 12. QUANTUM FIELD THEORY
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TitleGeometric and Topological Methods for Quantum Field Theory
Author(s)Ocampo, Hernan;Paycha, Sylvie;Vargas, Andr??s
PublicationBerlin, Heidelberg, 1. Imprint: Springer 2. Springer Berlin Heidelberg, 2005.
DescriptionXV, 230 p : online resource
Abstract NoteThis volume offers an introduction, in the form of four extensive lectures, to some recent developments in several active topics at the interface between geometry, topology and quantum field theory. The first lecture is by Christine Lescop on knot invariants and configuration spaces, in which a universal finite-type invariant for knots is constructed as a series of integrals over configuration spaces. This is followed by the contribution of Raimar Wulkenhaar on Euclidean quantum field theory from a statistical point of view. The author also discusses possible renormalization techniques on noncommutative spaces. The third lecture is by Anamaria Font and Stefan Theisen on string compactification with unbroken supersymmetry. The authors show that this requirement leads to internal spaces of special holonomy and describe Calabi-Yau manifolds in detail. The last lecture, by Thierry Fack, is devoted to a K-theory proof of the Atiyah-Singer index theorem and discusses some applications of K-theory to noncommutative geometry. These lectures notes, which are aimed in particular at graduate students in physics and mathematics, start with introductory material before presenting more advanced results. Each chapter is self-contained and can be read independently
ISBN,Price9783540315223
Keyword(s)1. COMPLEX MANIFOLDS 2. DIFFERENTIAL GEOMETRY 3. EBOOK 4. EBOOK - SPRINGER 5. Elementary particles (Physics) 6. Elementary Particles, Quantum Field Theory 7. Manifolds (Mathematics) 8. Manifolds and Cell Complexes (incl. Diff.Topology) 9. Mathematical Methods in Physics 10. PHYSICS 11. Quantum Field Theories, String Theory 12. QUANTUM FIELD THEORY 13. STRING THEORY
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7.     
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TitleQuantum Triangulations : Moduli Spaces, Strings, and Quantum Computing
Author(s)Carfora, Mauro;Marzuoli, Annalisa
PublicationBerlin, Heidelberg, 1. Imprint: Springer 2. Springer Berlin Heidelberg, 2012.
DescriptionXVII, 284 p. 90 illus., 10 illus. in color : online resource
Abstract NoteResearch on polyhedral manifolds often points to unexpected connections between very distinct aspects of Mathematics and Physics. In particular triangulated manifolds play quite a distinguished role in such settings as Riemann moduli space theory, strings and quantum gravity, topological quantum field theory, condensed matter physics, and critical phenomena. Not only do they provide a natural discrete analogue to the smooth manifolds on which physical theories are typically formulated, but their appearance is rather often a consequence of an underlying structure which naturally calls into play non-trivial aspects of representation theory, of complex analysis and topology in a way which makes manifest the basic geometric structures of the physical interactions involved. Yet, in most of the existing literature, triangulated manifolds are still merely viewed as a convenient discretization of a given physical theory to make it more amenable for numerical treatment. ?? The motivation for these lectures notes is thus to provide an approachable introduction to this topic, emphasizing the conceptual aspects, and probing, through a set of cases studies, the connection between triangulated manifolds and quantum physics to the deepest. ?? This volume addresses applied mathematicians and theoretical physicists working in the field of quantum geometry and its applications. ??
ISBN,Price9783642244407
Keyword(s)1. Classical and Quantum Gravitation, Relativity Theory 2. COMPLEX MANIFOLDS 3. EBOOK 4. EBOOK - SPRINGER 5. GRAVITATION 6. Manifolds (Mathematics) 7. Manifolds and Cell Complexes (incl. Diff.Topology) 8. Mathematical Applications in the Physical Sciences 9. MATHEMATICAL PHYSICS 10. PHYSICS 11. Physics, general 12. QUANTUM PHYSICS
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TitleAnalytical and Numerical Approaches to Mathematical Relativity
Author(s)Frauendiener, J??rg;Giulini, Domenico J. W;Perlick, Volker
PublicationBerlin, Heidelberg, 1. Imprint: Springer 2. Springer Berlin Heidelberg, 2006.
DescriptionXVII, 281 p : online resource
Abstract NoteToday, general relativity rates among the most accurately tested fundamental theories in all of physics. However, deficiencies in our mathematical and conceptual understanding still exist, and these partly hamper further progress. For this reason alone, but no less important from the point of view that a theory-based prediction should be regarded as no better than one's own structural understanding of the underlying theory, one should undertake serious investigations into the corresponding mathematical issues. This book contains a representative collection of surveys by experts in mathematical relativity writing about the current status of, and problems in, their fields. There are four contributions for each of the following mathematical areas: differential geometry and differential topology, analytical methods and differential equations, and numerical methods. This book addresses graduate students and specialist researchers alike
ISBN,Price9783540334842
Keyword(s)1. Classical and Quantum Gravitation, Relativity Theory 2. COMPLEX MANIFOLDS 3. DIFFERENTIAL GEOMETRY 4. EBOOK 5. EBOOK - SPRINGER 6. GRAVITATION 7. Manifolds (Mathematics) 8. Manifolds and Cell Complexes (incl. Diff.Topology) 9. Mathematical Methods in Physics 10. Numerical and Computational Physics, Simulation 11. PHYSICS
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9.     
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TitleMathematical Implications of Einstein-Weyl Causality
Author(s)Borchers, Hans J??rgen;Sen, Rathindra Nath
PublicationBerlin, Heidelberg, 1. Imprint: Springer 2. Springer Berlin Heidelberg, 2006.
DescriptionXII, 190 p. 37 illus : online resource
Abstract NoteThe present work is the first systematic attempt at answering the following fundamental question: what mathematical structures does Einstein-Weyl causality impose on a point-set that has no other previous structure defined on it? The authors propose an axiomatization of Einstein-Weyl causality (inspired by physics), and investigate the topological and uniform structures that it implies. Their final result is that a causal space is densely embedded in one that is locally a differentiable manifold. The mathematical level required of the reader is that of the graduate student in mathematical physics
ISBN,Price9783540376811
Keyword(s)1. Classical and Quantum Gravitation, Relativity Theory 2. COMPLEX MANIFOLDS 3. DIFFERENTIAL GEOMETRY 4. EBOOK 5. EBOOK - SPRINGER 6. GRAVITATION 7. Manifolds (Mathematics) 8. Manifolds and Cell Complexes (incl. Diff.Topology) 9. MATHEMATICAL PHYSICS 10. Theoretical, Mathematical and Computational Physics
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10.    
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TitleRenormalization of Quantum Field Theories with Non-linear Field Transformations : Proceedings of a Workshop, Held at Ringberg Castle Tegernsee, FRG, February 16???20, 1987
Author(s)Breitenlohner, Peter;Maison, Dieter;Sibold, Klaus
PublicationBerlin, Heidelberg, 1. Imprint: Springer 2. Springer Berlin Heidelberg, 1988.
DescriptionVI, 242 p. 11 illus : online resource
Abstract NoteThe characteristic feature of many models for field theories based on concepts of differential geometry is their nonlinearity. In this book a systematic exposition of nonlinear transformations in quantum field theory is given. The book starts with a short account of the renormalization theory with examples which can be handled successfully in four space-time dimensions. The second part is devoted to nonlinear sigma-models and their constructions in two dimensions. In the final section geometrical and cohomological methods and the relations to string theory are treated. This book is an important contribution towards rigorous definitions, and the mastering of nonlinear reparametrizations in agreement with the principles of quantum field theory will help to deal with anomalies, geometry and the like consistently and thus to understand better their implications for physics. The collection of papers addresses researchers and graduate students as well and will stimulate further work on the foundations of quantum field theory
ISBN,Price9783540391784
Keyword(s)1. COMPLEX MANIFOLDS 2. EBOOK 3. EBOOK - SPRINGER 4. Elementary particles (Physics) 5. Elementary Particles, Quantum Field Theory 6. Manifolds (Mathematics) 7. Manifolds and Cell Complexes (incl. Diff.Topology) 8. QUANTUM COMPUTERS 9. QUANTUM FIELD THEORY 10. Quantum Information Technology, Spintronics 11. QUANTUM PHYSICS 12. SPINTRONICS
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