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Author  Title  Accn#  Year  Item Type  Claims 
1 
Kimura, Taro 
Instanton Counting, Quantum Geometry and Algebra 
I11645 
2021 
eBook 

2 
Franchini, Fabio 
An Introduction to Integrable Techniques for OneDimensional Quantum Systems 
I10202 
2017 
eBook 

3 
Cardona, Alexander 
Quantization, Geometry and Noncommutative Structures in Mathematics and Physics 
I09980 
2017 
eBook 

4 
Rudolph, Gerd 
Differential Geometry and Mathematical Physics 
I09737 
2017 
eBook 

5 
Mizera, Sebastian 
Aspects of Scattering Amplitudes and Moduli Space Localization 
I09590 
2020 
eBook 

6 
Doubek, Martin 
Algebraic Structure of String Field Theory 
I09528 
2020 
eBook 

7 
Eckstein, Micha?? 
Spectral Action in Noncommutative Geometry 
I09061 
2018 
eBook 

8 
Ydri, Badis 
Lectures on Matrix Field Theory 
I08731 
2017 
eBook 

9 
Zhelnorovich, Vladimir A 
Theory of Spinors and Its Application in Physics and Mechanics 
I08606 
2019 
eBook 

10 
Esposito, Giampiero 
Complex General Relativity 
I10890 
2002 
eBook 


1.


Title  Instanton Counting, Quantum Geometry and Algebra 
Author(s)  Kimura, Taro 
Publication  Cham, Springer International Publishing, 2021. 
Description  XXIII, 285 p. 36 illus., 13 illus. in color : online resource 
Abstract Note  This book pedagogically describes recent developments in gauge theory, in particular fourdimensional N = 2 supersymmetric gauge theory, in relation to various fields in mathematics, including algebraic geometry, geometric representation theory, vertex operator algebras. The key concept is the instanton, which is a solution to the antiselfdual Yang???Mills equation in four dimensions. In the first part of the book, starting with the systematic description of the instanton, how to integrate out the instanton moduli space is explained together with the equivariant localization formula. It is then illustrated that this formalism is generalized to various situations, including quiver and fractional quiver gauge theory, supergroup gauge theory. The second part of the book is devoted to the algebraic geometric description of supersymmetric gauge theory, known as the Seiberg???Witten theory, together with string/Mtheory point of view. Based on its relation to integrable systems, how to quantize such a geometric structure via the ??deformation of gauge theory is addressed. The third part of the book focuses on the quantum algebraic structure of supersymmetric gauge theory. After introducing the free field realization of gauge theory, the underlying infinite dimensional algebraic structure is discussed with emphasis on the connection with representation theory of quiver, which leads to the notion of quiver Walgebra. It is then clarified that such a gauge theory construction of the algebra naturally gives rise to further affinization and elliptic deformation of Walgebra 
ISBN,Price  9783030761905 
Keyword(s)  1. ALGEBRAIC GEOMETRY
2. DIFFERENTIAL GEOMETRY
3. EBOOK
4. EBOOK  SPRINGER
5. Elementary particles (Physics)
6. Elementary Particles, Quantum Field Theory
7. GEOMETRY, DIFFERENTIAL
8. MATHEMATICAL PHYSICS
9. QUANTUM FIELD THEORY

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2.


Title  An Introduction to Integrable Techniques for OneDimensional Quantum Systems 
Author(s)  Franchini, Fabio 
Publication  Cham, Springer International Publishing, 2017. 
Description  XII, 180 p. 17 illus., 11 illus. in color : online resource 
Abstract Note  This book introduces the reader to basic notions of integrable techniques for onedimensional quantum systems. In a pedagogical way, a few examples of exactly solvable models are worked out to go from the coordinate approach to the Algebraic Bethe Ansatz, with some discussion on the finite temperature thermodynamics. The aim is to provide the instruments to approach more advanced books or to allow for a critical reading of research articles and the extraction of useful information from them. We describe the solution of the anisotropic XY spin chain; of the LiebLiniger model of bosons with contact interaction at zero and finite temperature; and of the XXZ spin chain, first in the coordinate and then in the algebraic approach. To establish the connection between the latter and the solution of two dimensional classical models, we also introduce and solve the 6vertex model. Finally, the low energy physics of these integrable models is mapped into the corresponding conformal field theory. Through its style and the choice of topics, this book tries to touch all fundamental ideas behind integrability and is meant for students and researchers interested either in an introduction to later delve in the advance aspects of Bethe Ansatz or in an overview of the topic for broadening their culture 
ISBN,Price  9783319484877 
Keyword(s)  1. ALGEBRAIC GEOMETRY
2. CONDENSED MATTER
3. CONDENSED MATTER PHYSICS
4. EBOOK
5. EBOOK  SPRINGER
6. Mathematical Methods in Physics
7. MATHEMATICAL PHYSICS
8. PHYSICS

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Call#  Status  Issued To  Return Due On  Physical Location 
I10202 


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3.


Title  Quantization, Geometry and Noncommutative Structures in Mathematics and Physics 
Author(s)  Cardona, Alexander;Morales, Pedro;Ocampo, Hern??n;Paycha, Sylvie;Reyes Lega, Andr??s F 
Publication  Cham, Springer International Publishing, 2017. 
Description  X, 341 p. 6 illus : online resource 
Abstract Note  This monograph presents various ongoing approaches to the vast topic of quantization, which is the process of forming a quantum mechanical system starting from a classical one, and discusses their numerous fruitful interactions with mathematics. The opening chapter introduces the various forms of quantization and their interactions with each other and with mathematics. A first approach to quantization, called deformation quantization, consists of viewing the Planck constant as a small parameter. This approach provides a deformation of the structure of the algebra of classical observables rather than a radical change in the nature of the observables. When symmetries come into play, deformation quantization needs to be merged with group actions, which is presented in chapter 2, by Simone Gutt. The noncommutativity arising from quantization is the main concern of noncommutative geometry. Allowing for the presence of symmetries requires working with principal fiber bundles in a noncommutative setup, where Hopf algebras appear naturally. This is the topic of chapter 3, by Christian Kassel. Nichols algebras, a special type of Hopf algebras, are the subject of chapter 4, by Nicol??s Andruskiewitsch. ?? The purely algebraic approaches given in the previous chapters do not take the geometry of spacetime into account. For this purpose a special treatment using a more geometric point of view is required. An approach to field quantization on curved spacetime, with applications to cosmology, is presented in chapter 5 in an account of the lectures of Abhay Ashtekar that brings a complementary point of view to noncommutativity. An alternative quantization procedure is known under the name of string theory. In chapter 6 its supersymmetric version is presented. Superstrings have drawn the attention of many mathematicians, due to its various fruitful interactions with algebraic geometry, some of which are described here. The remaining chapters discuss further topics, as the BatalinVilkovisky formalism and direct products of spectral triples. This volume addresses both physicists and mathematicians and serves as an introduction to ongoing research in very active areas of mathematics and physics at the border line between geometry, topology, algebra and quantum field theory 
ISBN,Price  9783319654270 
Keyword(s)  1. ALGEBRAIC GEOMETRY
2. EBOOK
3. EBOOK  SPRINGER
4. MATHEMATICAL PHYSICS
5. Quantum Field Theories, String Theory
6. QUANTUM FIELD THEORY
7. STRING THEORY

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Call#  Status  Issued To  Return Due On  Physical Location 
I09980 


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4.


Title  Differential Geometry and Mathematical Physics : Part II. Fibre Bundles, Topology and Gauge Fields 
Author(s)  Rudolph, Gerd;Schmidt, Matthias 
Publication  Dordrecht, Springer Netherlands, 2017. 
Description  XVI, 830 p. 15 illus., 2 illus. in color : online resource 
Abstract Note  The book is devoted to the study of the geometrical and topological structure of gauge theories. It consists of the following three building blocks:  Geometry and topology of fibre bundles,  Clifford algebras, spin structures and Dirac operators,  Gauge theory. Written in the style of a mathematical textbook, it combines a comprehensive presentation of the mathematical foundations with a discussion of a variety of advanced topics in gauge theory. The first building block includes a number of specific topics, like invariant connections, universal connections, Hstructures and the Postnikov approximation of classifying spaces. Given the great importance of Dirac operators in gauge theory, a complete proof of the AtiyahSinger Index Theorem is presented. The gauge theory part contains the study of YangMills equations (including the theory of instantons and the classical stability analysis), the discussion of various models with matter fields (including magnetic monopoles, the SeibergWitten model and dimensional reduction) and the investigation of the structure of the gauge orbit space. The final chapter is devoted to elements of quantum gauge theory including the discussion of the Gribov problem, anomalies and the implementation of the nongeneric gauge orbit strata in the framework of Hamiltonian lattice gauge theory. The book is addressed both to physicists and mathematicians. It is intended to be accessible to students starting from a graduate level 
ISBN,Price  9789402409598 
Keyword(s)  1. ALGEBRAIC GEOMETRY
2. ALGEBRAIC TOPOLOGY
3. DIFFERENTIAL GEOMETRY
4. EBOOK
5. EBOOK  SPRINGER
6. Elementary particles (Physics)
7. Elementary Particles, Quantum Field Theory
8. Mathematical Methods in Physics
9. MATHEMATICAL PHYSICS
10. PHYSICS
11. QUANTUM FIELD THEORY

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Call#  Status  Issued To  Return Due On  Physical Location 
I09737 


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5.


Title  Aspects of Scattering Amplitudes and Moduli Space Localization 
Author(s)  Mizera, Sebastian 
Publication  Cham, Springer International Publishing, 2020. 
Description  XVII, 134 p. 18 illus., 14 illus. in color : online resource 
Abstract Note  This thesis proposes a new perspective on scattering amplitudes in quantum field theories. Their standard formulation in terms of sums over Feynman diagrams is replaced by a computation of geometric invariants, called intersection numbers, on moduli spaces of Riemann surfaces. It therefore gives a physical interpretation of intersection numbers, which have been extensively studied in the mathematics literature in the context of generalized hypergeometric functions. This book explores physical consequences of this formulation, such as recursion relations, connections to geometry and string theory, as well as a phenomenon called moduli space localization. After reviewing necessary mathematical background, including topology of moduli spaces of Riemann spheres with punctures and its fundamental group, the definition and properties of intersection numbers are presented. A comprehensive list of applications and relations to other objects is given, including those to scattering amplitudes in open and closedstring theories. The highlights of the thesis are the results regarding localization properties of intersection numbers in two opposite limits: in the low and the highenergy expansion. In order to facilitate efficient computations of intersection numbers the author introduces recursion relations that exploit fibration properties of the moduli space. These are formulated in terms of socalled braid matrices that encode the information of how points braid around each other on the corresponding Riemann surface. Numerous application of this approach are presented for computation of scattering amplitudes in various gauge and gravity theories. This book comes with an extensive appendix that gives a pedagogical introduction to the topic of homologies with coefficients in a local system 
ISBN,Price  9783030530105 
Keyword(s)  1. ALGEBRAIC GEOMETRY
2. EBOOK
3. EBOOK  SPRINGER
4. Elementary particles (Physics)
5. Elementary Particles, Quantum Field Theory
6. MATHEMATICAL PHYSICS
7. QUANTUM FIELD THEORY
8. Theoretical, Mathematical and Computational Physics

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Call#  Status  Issued To  Return Due On  Physical Location 
I09590 


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6.


Title  Algebraic Structure of String Field Theory 
Author(s)  Doubek, Martin;Jur??o, Branislav;Markl, Martin;Sachs, Ivo 
Publication  Cham, Springer International Publishing, 2020. 
Description  XI, 221 p. 49 illus., 3 illus. in color : online resource 
Abstract Note  This book gives a modern presentation of modular operands and their role in string field theory. The authors aim to outline the arguments from the perspective of homotopy algebras and their operadic origin. Part I reviews string field theory from the point of view of homotopy algebras, including Ainfinity algebras, loop homotopy (quantum Linfinity) and IBLinfinity algebras governing its structure. Within this framework, the covariant construction of a string field theory naturally emerges as composition of two morphisms of particular odd modular operads. This part is intended primarily for researchers and graduate students who are interested in applications of higher algebraic structures to strings and quantum field theory. Part II contains a comprehensive treatment of the mathematical background on operads and homotopy algebras in a broader context, which should appeal also to mathematicians who are not familiar with string theory 
ISBN,Price  9783030530563 
Keyword(s)  1. ALGEBRAIC GEOMETRY
2. EBOOK
3. EBOOK  SPRINGER
4. Mathematical Methods in Physics
5. MATHEMATICAL PHYSICS
6. PHYSICS
7. Theoretical, Mathematical and Computational Physics

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Call#  Status  Issued To  Return Due On  Physical Location 
I09528 


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7.


Title  Spectral Action in Noncommutative Geometry 
Author(s)  Eckstein, Micha??;Iochum, Bruno 
Publication  Cham, Springer International Publishing, 2018. 
Description  XIV, 155 p. 3 illus : online resource 
Abstract Note  What is spectral action, how to compute it and what are the known examples? This book offers a guided tour through the mathematical habitat of noncommutative geometry ?? la Connes, deliberately unveiling the answers to these questions. After a brief preface flashing the panorama of the spectral approach, a concise primer on spectral triples is given. Chapter 2 is designed to serve as a toolkit for computations. The third chapter offers an indepth view into the subtle links between the asymptotic expansions of traces of heat operators and meromorphic extensions of the associated spectral zeta functions. Chapter 4 studies the behaviour of the spectral action under fluctuations by gauge potentials. A subjective list of open problems in the field is spelled out in the fifth Chapter. The book concludes with an appendix including some auxiliary tools from geometry and analysis, along with examples of spectral geometries. The book serves both as a compendium for researchers in the domain of noncommutative geometry and an invitation to mathematical physicists looking for new concepts 
ISBN,Price  9783319947884 
Keyword(s)  1. Abstract Harmonic Analysis
2. ALGEBRAIC GEOMETRY
3. Classical and Quantum Gravitation, Relativity Theory
4. EBOOK
5. EBOOK  SPRINGER
6. Elementary particles (Physics)
7. Elementary Particles, Quantum Field Theory
8. GRAVITATION
9. HARMONIC ANALYSIS
10. Mathematical Methods in Physics
11. MATHEMATICAL PHYSICS
12. PHYSICS
13. QUANTUM FIELD THEORY

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Call#  Status  Issued To  Return Due On  Physical Location 
I09061 


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8.


Title  Lectures on Matrix Field Theory 
Author(s)  Ydri, Badis 
Publication  Cham, Springer International Publishing, 2017. 
Description  XII, 352 p. 8 illus., 6 illus. in color : online resource 
Abstract Note  These lecture notes provide a systematic introduction to matrix models of quantum field theories with noncommutative and fuzzy geometries.?? The book initially focuses on the matrix formulation of noncommutative and fuzzy spaces, followed by a description of the nonperturbative treatment of the corresponding field theories. As an example, the phase structure of noncommutative phifour theory is treated in great detail, with a separate chapter on the multitrace approach. The last chapter offers a general introduction to noncommutative gauge theories, while two appendices round out the text. Primarily written as a selfstudy guide for postgraduate students ??? with the aim of pedagogically introducing them to key analytical and numerical tools, as well as useful physical models in applications ??? these lecture notes will also benefit experienced researchers by providing a reference guide to the fundamentals of noncommutative field theory with an emphasis on matrix models and fuzzy geometries 
ISBN,Price  9783319460031 
Keyword(s)  1. ALGEBRAIC GEOMETRY
2. Computer science???Mathematics
3. EBOOK
4. EBOOK  SPRINGER
5. Math Applications in Computer Science
6. MATHEMATICAL PHYSICS
7. Quantum Field Theories, String Theory
8. QUANTUM FIELD THEORY
9. QUANTUM PHYSICS
10. STRING THEORY

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Call#  Status  Issued To  Return Due On  Physical Location 
I08731 


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9.


Title  Theory of Spinors and Its Application in Physics and Mechanics 
Author(s)  Zhelnorovich, Vladimir A 
Publication  Cham, Springer International Publishing, 2019. 
Description  XVI, 392 p : online resource 
Abstract Note  This book contains a systematic exposition of the theory of spinors in finitedimensional Euclidean and Riemannian spaces. The applications of spinors in field theory and relativistic mechanics of continuous media are considered. The main mathematical part is connected with the study of invariant algebraic and geometric relations between spinors and tensors. The theory of spinors and the methods of the tensor representation of spinors and spinor equations are thoroughly expounded in fourdimensional and threedimensional spaces. Very useful and important relations are derived that express the derivatives of the spinor fields in terms of the derivatives of various tensor fields. The problems associated with an invariant description of spinors as objects that do not depend on the choice of a coordinate system are addressed in detail. As an application, the author considers an invariant tensor formulation of certain classes of differential spinor equations containing, in particular, the most important spinor equations of field theory and quantum mechanics. Exact solutions of the Einstein???Dirac equations, nonlinear Heisenberg???s spinor equations, and equations for relativistic spin fluids are given. The book presents a large body of factual material and is suited for use as a handbook. It is intended for specialists in theoretical physics, as well as for students and postgraduate students of physical and mathematical specialties 
ISBN,Price  9783030278366 
Keyword(s)  1. ALGEBRAIC GEOMETRY
2. COSMOLOGY
3. EBOOK
4. EBOOK  SPRINGER
5. Elementary particles (Physics)
6. Elementary Particles, Quantum Field Theory
7. Mathematical Methods in Physics
8. MATHEMATICAL PHYSICS
9. PHYSICS
10. QUANTUM FIELD THEORY

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Call#  Status  Issued To  Return Due On  Physical Location 
I08606 


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10.
 
Title  Complex General Relativity 
Author(s)  Esposito, Giampiero 
Publication  Dordrecht, Springer Netherlands, 2002. 
Description  XII, 206 p : online resource 
Abstract Note  This book is written for theoretical and mathematical physicists and mat maticians interested in recent developments in complex general relativity and their application to classical and quantum gravity. Calculations are presented by paying attention to those details normally omitted in research papers, for pedagogical r sons. Familiarity with fibrebundle theory is certainly helpful, but in many cases I only rely on twospinor calculus and conformally invariant concepts in gravitational physics. The key concepts the book is devoted to are complex manifolds, spinor techniques, conformal gravity, ?planes, ?surfaces, Penrose transform, complex 3 1 ??? ??? spacetime models with nonvanishing torsion, spin fields and spin potentials. 2 2 Problems have been inserted at the end, to help the reader to check his und standing of these topics. Thus, I can find at least four reasons for writing yet another book on spinor and twistor methods in general relativity: (i) to write a textbook useful to  ginning graduate students and research workers, where twocomponent spinor c culus is the unifying mathematical language 
ISBN,Price  9780306471186 
Keyword(s)  1. ALGEBRAIC GEOMETRY
2. Applications of Mathematics
3. APPLIED MATHEMATICS
4. Classical and Quantum Gravitation, Relativity Theory
5. DIFFERENTIAL GEOMETRY
6. EBOOK
7. EBOOK  SPRINGER
8. ENGINEERING MATHEMATICS
9. GRAVITATION
10. MATHEMATICAL PHYSICS
11. PARTIAL DIFFERENTIAL EQUATIONS
12. Theoretical, Mathematical and Computational Physics

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Call#  Status  Issued To  Return Due On  Physical Location 
I10890 


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