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1 Mehta, Umang Postmodern Fermi Liquids I13199 2024 eBook  
2 Govindarajan, T. R Geometry and Topology of Low Dimensional Systems I13148 2024 eBook  
3 Dhurandhar, Sanjeev Understanding Mathematical Concepts in Physics I13100 2024 eBook  
4 Wang, Jielong Multiscale Multibody Dynamics I12683 2023 eBook  
5 Fuchs, J??rgen String-Net Construction of RCFT Correlators I12264 2022 Book  
6 Saller, Heinrich Operational Symmetries I10249 2017 eBook  
7 Schwichtenberg, Jakob Physics from Symmetry I09443 2018 eBook  
8 Cassinelli, Gianni The Theory of Symmetry Actions in Quantum Mechanics I11185 2004 eBook  
9 Ali, Syed T Coherent States, Wavelets and Their Generalizations I10838 2000 eBook  
10 Teodorescu, Petre P Applications of the Theory of Groups in Mechanics and Physics I10502 2004 eBook  
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TitlePostmodern Fermi Liquids
Author(s)Mehta, Umang
PublicationCham, 1. Imprint: Springer 2. Springer Nature Switzerland, 2024.
DescriptionXV, 102 p. 9 illus., 8 illus. in color : online resource
Abstract NoteThis thesis develops a new approach to Fermi liquids based on the mathematical formalism of coadjoint orbits, allowing Landau???s Fermi liquid theory to be recast in a simple and elegant way as a field theory. The theory of Fermi liquids is a cornerstone of condensed matter physics with many applications, but efforts to cast Landau???s Fermi liquid theory in the modern language of effective field theory suffer from technical and conceptual difficulties: the Fermi surface seems to defy a simple effective field theory description. This thesis reviews the recently-developed formalism for Fermi liquids that exploits an underlying structure described by the group of canonical transformations of a single particle phase space. This infinite-dimensional group governs the space of states of zero temperature Fermi liquids and allows one to write down a nonlinear, bosonized action that reproduces Landau???s kinetic theory in the classical limit. The thesis then describes how that Fermi liquid theory can essentially be thought of as a non-trivial representation of the Lie group of canonical transformations, bringing it within the fold of effective theories in many-body physics whose structure is determined by symmetries. After analyzing the benefits and limitations of this geometric formalism, pathways to extensions of the formalism to include superconducting and magnetic phases, as well as applications to the problem of non-Fermi liquids, are discussed. The thesis begins with a pedagogical review of Fermi liquid theory and concludes with a discussion on possible future directions for Fermi surface physics, and more broadly, the usefulness of diffeomorphism groups in condensed matter physics
ISBN,Price9783031724039
Keyword(s)1. EBOOK 2. EBOOK - SPRINGER 3. Elementary particles (Physics) 4. Elementary Particles, Quantum Field Theory 5. LIE GROUPS 6. LOW TEMPERATURE PHYSICS 7. LOW TEMPERATURES 8. MATHEMATICAL PHYSICS 9. QUANTUM ELECTRODYNAMICS 10. Quantum Electrodynamics, Relativistic and Many-body Calculations 11. QUANTUM FIELD THEORY 12. Quantum Fluids and Solids 13. QUANTUM STATISTICS 14. TOPOLOGICAL GROUPS 15. Topological Groups and Lie Groups
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TitleGeometry and Topology of Low Dimensional Systems : Chern-Simons Theory with Applications
Author(s)Govindarajan, T. R;Ramadevi, Pichai
PublicationCham, 1. Imprint: Springer 2. Springer International Publishing, 2024.
DescriptionXIV, 167 p. 48 illus., 9 illus. in color : online resource
Abstract NoteThis book introduces the field of topology, a branch of mathematics that explores the properties of geometric space, with a focus on low-dimensional systems. The authors discuss applications in various areas of physics. The first chapters of the book cover the formal aspects of topology, including classes, homotopic groups, metric spaces, and Riemannian and pseudo-Riemannian geometry. These topics are essential for understanding the theoretical concepts and notations used in the next chapters of the book. The applications encompass defects in crystalline structures, space topology, spin statistics, Braid group, Chern-Simons field theory, and 3D gravity, among others. This self-contained book provides all the necessary additional material for both physics and mathematics students. The presentation is enriched with examples and exercises, making it accessible for readers to grasp the concepts with ease. The authors adopt a pedagogical approach, posing many unsolved questions in simple situations that can serve as challenging projects for students. Suitable for a one-semester postgraduate level course, this text is ideal for teaching purposes
ISBN,Price9783031595011
Keyword(s)1. ASSOCIATIVE ALGEBRAS 2. Associative rings 3. Associative Rings and Algebras 4. EBOOK 5. EBOOK - SPRINGER 6. Elementary particles (Physics) 7. Elementary Particles, Quantum Field Theory 8. LIE GROUPS 9. MATHEMATICAL PHYSICS 10. QUANTUM FIELD THEORY 11. TOPOLOGICAL GROUPS 12. Topological Groups and Lie Groups 13. TOPOLOGY
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TitleUnderstanding Mathematical Concepts in Physics : Insights from Geometrical and Numerical Approaches
Author(s)Dhurandhar, Sanjeev
PublicationCham, 1. Imprint: Springer 2. Springer Nature Switzerland, 2024.
DescriptionXVI, 351 p. 57 illus., 42 illus. in color : online resource
Abstract NoteModern mathematics has become an essential part of today???s physicist???s arsenal and this book covers several relevant such topics. The primary aim of this book is to present key mathematical concepts in an intuitive way with the help of geometrical and numerical methods - understanding is the key. Not all differential equations can be solved with standard techniques. Examples illustrate how geometrical insights and numerical methods are useful in understanding differential equations in general but are indispensable when extracting relevant information from equations that do not yield to standard methods. Adopting a numerical approach to complex analysis it is shown that Cauchy???s theorem, the Cauchy integral formula, the residue theorem, etc. can be verified by performing hands-on computations with Python codes. Figures elucidate the concept of poles and essential singularities. Further the book covers topology, Hilbert spaces, Fourier transforms (discussing how fast Fourier transform works), modern differential geometry, Lie groups and Lie algebras, probability and useful probability distributions, and statistical detection of signals. Novel features include: (i) Topology is introduced via the notion of continuity on the real line which then naturally leads to topological spaces. (ii) Data analysis in a differential geometric framework and a general description of ??2 discriminators in terms of vector bundles. This book is targeted at physics graduate students and at theoretical (and possibly experimental) physicists. Apart from research students, this book is also useful to active physicists in their research and teaching
ISBN,Price9783031603945
Keyword(s)1. ANALYSIS 2. DIFFERENTIAL EQUATIONS 3. EBOOK 4. EBOOK - SPRINGER 5. FOURIER ANALYSIS 6. LIE GROUPS 7. MATHEMATICAL ANALYSIS 8. MATHEMATICAL PHYSICS 9. Theoretical, Mathematical and Computational Physics 10. TOPOLOGICAL GROUPS 11. Topological Groups and Lie Groups
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TitleMultiscale Multibody Dynamics : Motion Formalism Implementation
Author(s)Wang, Jielong
PublicationSingapore, 1. Imprint: Springer 2. Springer Nature Singapore, 2023.
DescriptionXVI, 359 p. 80 illus., 79 illus. in color : online resource
Abstract NoteThis book presents a novel theory of multibody dynamics with distinct features, including unified continuum theory, multiscale modeling technology of multibody system, and motion formalism implementation. All these features together with the introductions of fundamental concepts of vector, dual vector, tensor, dual tensor, recursive descriptions of joints, and the higher-order implicit solvers formulate the scope of the book???s content. In this book, a multibody system is defined as a set consisted of flexible and rigid bodies which are connected by any kinds of joints or constraints to achieve the desired motion. Generally, the motion of multibody system includes the translation and rotation; it is more efficient to describe the motion by using the dual vector or dual tensor directly instead of defining two types of variables, the translation and rotation separately. Furthermore, this book addresses the detail of motion formalism and its finite element implementation of the solid, shell-like, and beam-like structures. It also introduces the fundamental concepts of mechanics, such as the definition of vector, dual vector, tensor, and dual tensor, briefly. Without following the Einstein summation convention, the first- and second-order tensor operations in this book are depicted by linear algebraic operation symbols of row array, column array, and two-dimensional matrix, making these operations easier to understand. In addition, for the integral of governing equations of motion, a set of ordinary differential equations for the finite element-based discrete system, the book discussed the implementation of implicit solvers in detail and introduced the well-developed RADAU IIA algorithms based on post-error estimation to make the contents of the book complete. The intended readers of this book are senior engineers and graduate students in related engineering fields
ISBN,Price9789811984419
Keyword(s)1. EBOOK - SPRINGER 2. LIE GROUPS 3. Mechanics, Applied 4. Multibody systems 5. Multibody Systems and Mechanical Vibrations 6. Solid Mechanics 7. SOLIDS 8. TOPOLOGICAL GROUPS 9. Topological Groups and Lie Groups 10. VIBRATION
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TitleString-Net Construction of RCFT Correlators
Author(s)Fuchs, J??rgen;Schweigert, Christoph;Yang, Yang
PublicationCham, 1. Imprint: Springer 2. Springer International Publishing, 2022.
DescriptionX, 123 p. 122 illus : online resource
Abstract NoteThis book studies using string-net models to accomplish a direct, purely two-dimensional, approach to correlators of two-dimensional rational conformal field theories. The authors obtain concise geometric expressions for the objects describing bulk and boundary fields in terms of idempotents in the cylinder category of the underlying modular fusion category, comprising more general classes of fields than is standard in the literature. Combining these idempotents with Frobenius graphs on the world sheet yields string nets that form a consistent system of correlators, i.e. a system of invariants under appropriate mapping class groups that are compatible with factorization. The authors extract operator products of field objects from specific correlators; the resulting operator products are natural algebraic expressions that make sense beyond semisimplicity. They also derive an Eckmann-Hilton relation internal to a braided category, thereby demonstrating the utility of string nets for understanding algebra in braided tensor categories. Finally, they introduce the notion of a universal correlator. This systematizes the treatment of situations in which different world sheets have the same correlator and allows for the definition of a more comprehensive mapping class group
ISBN,Price9783031146824
Keyword(s)1. EBOOK 2. EBOOK - SPRINGER 3. Elementary particles (Physics) 4. Elementary Particles, Quantum Field Theory 5. LIE GROUPS 6. MATHEMATICAL PHYSICS 7. QUANTUM FIELD THEORY 8. TOPOLOGICAL GROUPS 9. Topological Groups and Lie Groups
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TitleOperational Symmetries : Basic Operations in Physics
Author(s)Saller, Heinrich
PublicationCham, Springer International Publishing, 2017.
DescriptionXI, 574 p : online resource
Abstract NoteThis book describes the endeavour to relate the particle spectrum with representations of operational electroweak spacetime, in analogy to the atomic spectrum as characterizing representations of hyperbolic space. The spectrum of hyperbolic position space explains the properties of the nonrelativistic atoms; the spectrum of electroweak spacetime is hoped to explain those of the basic interactions and elementary particles. In this book, the theory of operational symmetries is developed from the numbers, from Plato???s and Kepler???s symmetries over the simple Lie groups to their applications in nonrelativistic, special relativistic and general relativistic quantum theories with the atomic spectrum for hyperbolic position and, in first attempts, the particle spectrum for electroweak spacetime. The standard model of elementary particles and interactions is characterized by a symmetry group. In general, as initiated by Weyl and stressed by Heisenberg, quantum theory can be built as a theory of operation groups and their unitary representations. In such a framework, time, position and spacetime is modeled by equivalence classes of symmetry groups. For a unification on this road, the quest is not for a final theory with a basic equation for basic particles, but for the basic operation group and its representations.
ISBN,Price9783319586649
Keyword(s)1. Classical and Quantum Gravitation, Relativity Theory 2. EBOOK 3. EBOOK - SPRINGER 4. GRAVITATION 5. LIE GROUPS 6. Mathematical Methods in Physics 7. MATHEMATICAL PHYSICS 8. PHYSICS 9. QUANTUM PHYSICS 10. TOPOLOGICAL GROUPS 11. Topological Groups, Lie Groups
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TitlePhysics from Symmetry
Author(s)Schwichtenberg, Jakob
PublicationCham, Springer International Publishing, 2018.
DescriptionXXI, 287 p. 28 illus., 15 illus. in color : online resource
Abstract NoteThis is a textbook that derives the fundamental theories of physics from symmetry. It starts by introducing, in a completely self-contained way, all mathematical tools needed to use symmetry ideas in physics. Thereafter, these tools are put into action and by using symmetry constraints, the fundamental equations of Quantum Mechanics, Quantum Field Theory, Electromagnetism, and Classical Mechanics are derived. As a result, the reader is able to understand the basic assumptions behind, and the connections between the modern theories of physics. The book concludes with first applications of the previously derived equations. Thanks to the input of readers from around the world, this second edition has been purged of typographical errors and also contains several revised sections with improved explanations.??
ISBN,Price9783319666310
Keyword(s)1. EBOOK 2. EBOOK - SPRINGER 3. LIE GROUPS 4. Mathematical Methods in Physics 5. MATHEMATICAL PHYSICS 6. NUCLEAR PHYSICS 7. Particle and Nuclear Physics 8. PHYSICS 9. TOPOLOGICAL GROUPS 10. Topological Groups, Lie Groups
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TitleThe Theory of Symmetry Actions in Quantum Mechanics : with an Application to the Galilei Group
Author(s)Cassinelli, Gianni;Vito, Ernesto;Levrero, Alberto;Lahti, Pekka J
PublicationBerlin, Heidelberg, Springer Berlin Heidelberg, 2004.
DescriptionXII, 111 p : online resource
Abstract NoteThis is a book about representing symmetry in quantum mechanics. The book is on a graduate and/or researcher level and it is written with an attempt to be concise, to respect conceptual clarity and mathematical rigor. The basic structures of quantum mechanics are used to identify the automorphism group of quantum mechanics. The main concept of a symmetry action is defined as a group homomorphism from a given group, the group of symmetries, to the automorphism group of quantum mechanics. The structure of symmetry actions is determined under the assumption that the symmetry group is a Lie group. The Galilei invariance is used to illustrate the general theory by giving a systematic presentation of a Galilei invariant elementary particle. A brief description of the Galilei invariant wave equations is also given
ISBN,Price9783540445098
Keyword(s)1. EBOOK 2. EBOOK - SPRINGER 3. GROUP THEORY 4. Group Theory and Generalizations 5. LIE GROUPS 6. Mathematical Methods in Physics 7. PHYSICS 8. QUANTUM PHYSICS 9. TOPOLOGICAL GROUPS 10. Topological Groups, Lie Groups
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TitleCoherent States, Wavelets and Their Generalizations
Author(s)Ali, Syed T;Antoine, J-P;Gazeau, Jean-Perre
PublicationNew York, NY, Springer New York, 2000.
DescriptionXIII, 418 p : online resource
Abstract NoteNitya kaaler utshab taba Bishyer-i-dipaalika Aami shudhu tar-i-mateer pradeep Jaalao tahaar shikhaa 1 - Tagore Should authors feel compelled to justify the writing of yet another book? In an overpopulated world, should parents feel compelled to justify bringing forth yet another child? Perhaps not! But an act of creation is also an act of love, and a love story can always be happily shared. In writing this book, it has been our feeling that, in all of the wealth of material on coherent states and wavelets, there exists a lack of a discern?? able, unifying mathematical perspective. The use of wavelets in research and technology has witnessed explosive growth in recent years, while the use of coherent states in numerous areas of theoretical and experimental physics has been an established trend for decades. Yet it is not at all un?? common to find practitioners in either one of the two disciplines who are hardly aware of one discipline's links to the other. Currently, many books are on the market that treat the subject of wavelets from a wide range of perspectives and with windows on one or several areas of a large spectrum IThine is an eternal celebration '" A cosmic Festival of Lights! '" Therein I am a mere flicker of a wicker lamp, , . 0 kindle its flame (my Master!), vi Preface of possible applications
ISBN,Price9781461212584
Keyword(s)1. EBOOK 2. EBOOK - SPRINGER 3. LIE GROUPS 4. QUANTUM COMPUTERS 5. Quantum Information Technology, Spintronics 6. QUANTUM PHYSICS 7. SPINTRONICS 8. TOPOLOGICAL GROUPS 9. Topological Groups, Lie Groups
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TitleApplications of the Theory of Groups in Mechanics and Physics
Author(s)Teodorescu, Petre P;Nicorovici, Nicolae-A.P
PublicationDordrecht, Springer Netherlands, 2004.
DescriptionXIV, 446 p. 17 illus : online resource
Abstract NoteThe notion of group is fundamental in our days, not only in mathematics, but also in classical mechanics, electromagnetism, theory of relativity, quantum mechanics, theory of elementary particles, etc. This notion has developed during a century and this development is connected with the names of great mathematicians as E. Galois, A. L. Cauchy, C. F. Gauss, W. R. Hamilton, C. Jordan, S. Lie, E. Cartan, H. Weyl, E. Wigner, and of many others. In mathematics, as in other sciences, the simple and fertile ideas make their way with difficulty and slowly; however, this long history would have been of a minor interest, had the notion of group remained connected only with rather restricted domains of mathematics, those in which it occurred at the beginning. But at present, groups have invaded almost all mathematical disciplines, mechanics, the largest part of physics, of chemistry, etc. We may say, without exaggeration, that this is the most important idea that occurred in mathematics since the invention of infinitesimal calculus; indeed, the notion of group expresses, in a precise and operational form, the vague and universal ideas of regularity and symmetry. The notion of group led to a profound understanding of the character of the laws which govern natural phenomena, permitting to formulate new laws, correcting certain inadequate formulations and providing unitary and non?? contradictory formulations for the investigated phenomena
ISBN,Price9781402020476
Keyword(s)1. Applications of Mathematics 2. APPLIED MATHEMATICS 3. EBOOK 4. EBOOK - SPRINGER 5. ENGINEERING MATHEMATICS 6. Heavy ions 7. LIE GROUPS 8. MATHEMATICAL PHYSICS 9. NUCLEAR PHYSICS 10. Nuclear Physics, Heavy Ions, Hadrons 11. PARTIAL DIFFERENTIAL EQUATIONS 12. Theoretical, Mathematical and Computational Physics 13. TOPOLOGICAL GROUPS 14. Topological Groups, Lie Groups
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