Frobenius Algebras and 2-D Topological Quantum Field Theories - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Frobenius Algebras and 2-D Topological Quantum Field Theories write by Joachim Kock. This book was released on 2004. Frobenius Algebras and 2-D Topological Quantum Field Theories available in PDF, EPUB and Kindle. This 2003 book describes a striking connection between topology and algebra, namely that 2D topological quantum field theories are equivalent to commutative Frobenius algebras. The precise formulation of the theorem and its proof is given in terms of monoidal categories, and the main purpose of the book is to develop these concepts from an elementary level, and more generally serve as an introduction to categorical viewpoints in mathematics. Rather than just proving the theorem, it is shown how the result fits into a more general pattern concerning universal monoidal categories for algebraic structures. Throughout, the emphasis is on the interplay between algebra and topology, with graphical interpretation of algebraic operations, and topological structures described algebraically in terms of generators and relations. The book will prove valuable to students or researchers entering this field who will learn a host of modern techniques that will prove useful for future work.
Lectures on Field Theory and Topology
Lectures on Field Theory and Topology - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Lectures on Field Theory and Topology write by Daniel S. Freed. This book was released on 2019-08-23. Lectures on Field Theory and Topology available in PDF, EPUB and Kindle. These lectures recount an application of stable homotopy theory to a concrete problem in low energy physics: the classification of special phases of matter. While the joint work of the author and Michael Hopkins is a focal point, a general geometric frame of reference on quantum field theory is emphasized. Early lectures describe the geometric axiom systems introduced by Graeme Segal and Michael Atiyah in the late 1980s, as well as subsequent extensions. This material provides an entry point for mathematicians to delve into quantum field theory. Classification theorems in low dimensions are proved to illustrate the framework. The later lectures turn to more specialized topics in field theory, including the relationship between invertible field theories and stable homotopy theory, extended unitarity, anomalies, and relativistic free fermion systems. The accompanying mathematical explanations touch upon (higher) category theory, duals to the sphere spectrum, equivariant spectra, differential cohomology, and Dirac operators. The outcome of computations made using the Adams spectral sequence is presented and compared to results in the condensed matter literature obtained by very different means. The general perspectives and specific applications fuse into a compelling story at the interface of contemporary mathematics and theoretical physics.
Homotopy Quantum Field Theory
Homotopy Quantum Field Theory - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Homotopy Quantum Field Theory write by Vladimir G. Turaev. This book was released on 2010. Homotopy Quantum Field Theory available in PDF, EPUB and Kindle. Homotopy Quantum Field Theory (HQFT) is a branch of Topological Quantum Field Theory founded by E. Witten and M. Atiyah. It applies ideas from theoretical physics to study principal bundles over manifolds and, more generally, homotopy classes of maps from manifolds to a fixed target space. This book is the first systematic exposition of Homotopy Quantum Field Theory. It starts with a formal definition of an HQFT and provides examples of HQFTs in all dimensions. The main body of the text is focused on $2$-dimensional and $3$-dimensional HQFTs. A study of these HQFTs leads to new algebraic objects: crossed Frobenius group-algebras, crossed ribbon group-categories, and Hopf group-coalgebras. These notions and their connections with HQFTs are discussed in detail. The text ends with several appendices including an outline of recent developments and a list of open problems. Three appendices by M. Muger and A. Virelizier summarize their work in this area. The book is addressed to mathematicians, theoretical physicists, and graduate students interested in topological aspects of quantum field theory. The exposition is self-contained and well suited for a one-semester graduate course. Prerequisites include only basics of algebra and topology.
Frobenius Algebras and 2D Topological Quantum Field Theories
Frobenius Algebras and 2D Topological Quantum Field Theories - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Frobenius Algebras and 2D Topological Quantum Field Theories write by Joachim Kock. This book was released on 2003. Frobenius Algebras and 2D Topological Quantum Field Theories available in PDF, EPUB and Kindle. Proves striking results connecting topology and algebra and shows how the result fits into a more general pattern. The book will prove valuable to students or researchers entering this field who will learn a host of modern techniques. There are numerous exercises and examples making the book suitable for teaching.
Dirichlet Branes and Mirror Symmetry
Dirichlet Branes and Mirror Symmetry - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Dirichlet Branes and Mirror Symmetry write by . This book was released on 2009. Dirichlet Branes and Mirror Symmetry available in PDF, EPUB and Kindle. Research in string theory has generated a rich interaction with algebraic geometry, with exciting work that includes the Strominger-Yau-Zaslow conjecture. This monograph builds on lectures at the 2002 Clay School on Geometry and String Theory that sought to bridge the gap between the languages of string theory and algebraic geometry.
