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Author: Alberto S. Cattaneo Publisher: Springer Science & Business Media ISBN: 081764735X Category : Mathematics Languages : en Pages : 371
Book Description
This book is centered around higher algebraic structures stemming from the work of Murray Gerstenhaber and Jim Stasheff that are now ubiquitous in various areas of mathematics— such as algebra, algebraic topology, differential geometry, algebraic geometry, mathematical physics— and in theoretical physics such as quantum field theory and string theory. These higher algebraic structures provide a common language essential in the study of deformation quantization, theory of algebroids and groupoids, symplectic field theory, and much more. Each contribution in this volume expands on the ideas of Gerstenhaber and Stasheff. The volume is intended for post-graduate students, mathematical and theoretical physicists, and mathematicians interested in higher structures.
Author: Alberto S. Cattaneo Publisher: Springer Science & Business Media ISBN: 081764735X Category : Mathematics Languages : en Pages : 371
Book Description
This book is centered around higher algebraic structures stemming from the work of Murray Gerstenhaber and Jim Stasheff that are now ubiquitous in various areas of mathematics— such as algebra, algebraic topology, differential geometry, algebraic geometry, mathematical physics— and in theoretical physics such as quantum field theory and string theory. These higher algebraic structures provide a common language essential in the study of deformation quantization, theory of algebroids and groupoids, symplectic field theory, and much more. Each contribution in this volume expands on the ideas of Gerstenhaber and Stasheff. The volume is intended for post-graduate students, mathematical and theoretical physicists, and mathematicians interested in higher structures.
Author: Ralph M. Kaufmann Publisher: American Mathematical Society ISBN: 1470471426 Category : Mathematics Languages : en Pages : 332
Book Description
This volume contains the proceedings of the AMS Special Session on Higher Structures in Topology, Geometry, and Physics, held virtually on March 26–27, 2022. The articles give a snapshot survey of the current topics surrounding the mathematical formulation of field theories. There is an intricate interplay between geometry, topology, and algebra which captures these theories. The hallmark are higher structures, which one can consider as the secondary algebraic or geometric background on which the theories are formulated. The higher structures considered in the volume are generalizations of operads, models for conformal field theories, string topology, open/closed field theories, BF/BV formalism, actions on Hochschild complexes and related complexes, and their geometric and topological aspects.
Author: Jürgen Jost Publisher: Springer Science & Business Media ISBN: 3642005411 Category : Mathematics Languages : en Pages : 226
Book Description
"Geometry and Physics" addresses mathematicians wanting to understand modern physics, and physicists wanting to learn geometry. It gives an introduction to modern quantum field theory and related areas of theoretical high-energy physics from the perspective of Riemannian geometry, and an introduction to modern geometry as needed and utilized in modern physics. Jürgen Jost, a well-known research mathematician and advanced textbook author, also develops important geometric concepts and methods that can be used for the structures of physics. In particular, he discusses the Lagrangians of the standard model and its supersymmetric extensions from a geometric perspective.
Author: Tim Maudlin Publisher: ISBN: 0198701306 Category : Mathematics Languages : en Pages : 374
Book Description
Tim Maudlin sets out a completely new method for describing the geometrical structure of spaces, and thus a better mathematical tool for describing and understanding space-time. He presents a historical review of the development of geometry and topology, and then his original Theory of Linear Structures.
Author: Helmut Eschrig Publisher: Springer ISBN: 3642147003 Category : Science Languages : en Pages : 397
Book Description
A concise but self-contained introduction of the central concepts of modern topology and differential geometry on a mathematical level is given specifically with applications in physics in mind. All basic concepts are systematically provided including sketches of the proofs of most statements. Smooth finite-dimensional manifolds, tensor and exterior calculus operating on them, homotopy, (co)homology theory including Morse theory of critical points, as well as the theory of fiber bundles and Riemannian geometry, are treated. Examples from physics comprise topological charges, the topology of periodic boundary conditions for solids, gauge fields, geometric phases in quantum physics and gravitation.
Author: Alessandro Tomasiello Publisher: Cambridge University Press ISBN: 1108473733 Category : Science Languages : en Pages : 677
Book Description
A unified perspective on new and advanced mathematical techniques used in string theory research for graduate students and researchers.
Author: Alberto S. Cattaneo
Author: Alberto S. Cattaneo
Author: Ralph M. Kaufmann
Author: Jürgen Jost
Author: Michael Spivak
Author: Peter Szekeres
Author: Tim Maudlin
Author: Helmut Eschrig
Author: Alberto S. Cattaneo
Author: Tom Leinster
Author: Alessandro Tomasiello