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4 produkter
4 produkter
Inbunden, Engelska, 2012
1 609 kr
Skickas inom 5-8 vardagar
Conceptual progress in fundamental theoretical physics is linked with the search for the suitable mathematical structures that model the physical systems. Quantum field theory (QFT) has proven to be a rich source of ideas for mathematics for a long time. However, fundamental questions such as ``What is a QFT?'' did not have satisfactory mathematical answers, especially on spaces with arbitrary topology, fundamental for the formulation of perturbative string theory. This book contains a collection of papers highlighting the mathematical foundations of QFT and its relevance to perturbative string theory as well as the deep techniques that have been emerging in the last few years. The papers are organised under three main chapters: Foundations for Quantum Field Theory, Quantisation of Field Theories, and Two-Dimensional Quantum Field Theories. An introduction, written by the editors, provides an overview of the main underlying themes that bind together the papers in the volume.
Del 223 - Cambridge Studies in Advanced Mathematics
Equivariant Principal ∞-Bundles
Inbunden, Engelska, 2026
751 kr
Kommande
Principal bundles and their associated fiber bundles famously play a foundational role in both algebraic and differential topology, as well as in fundamental and solid-state physics. More recently, their equivariant and higher homotopy enhancements (gerbes) have been crucial in generalized cohomology theory and for the physics of extended solitons and topological phases. This text is the first to offer a unified perspective of, and introduction to, these topics, providing an insight into material previously scattered across the literature. After a self-contained account of the classical theory of equivariant principal bundles in modern topological groupoid language, the book develops, on the novel backdrop of cohesive higher topos theory, a powerful theory of equivariant principal higher bundles. It establishes new methods like the 'smooth Oka principle' and 'twisted Elmendorf theorem' to elegantly prove classification results and clarify the relation to proper equivariant generalized cohomology theories.
Inbunden, Engelska, 2026
1 725 kr
Kommande
Inbunden, Engelska, 2023
1 334 kr
Skickas inom 3-6 vardagar
This book presents a novel development of fundamental and fascinating aspects of algebraic topology and mathematical physics: "extra-ordinary" and further generalized cohomology theories enhanced to "twisted" and differential-geometric form, with focus on, firstly, their rational approximation by generalized Chern character maps, and then, the resulting charge quantization laws in higher n-form gauge field theories appearing in string theory and the classification of topological quantum materials.Although crucial for understanding famously elusive effects in strongly interacting physics, the relevant higher non-abelian cohomology theory ("higher gerbes") has had an esoteric reputation and remains underdeveloped.Devoted to this end, this book's theme is that various generalized cohomology theories are best viewed through their classifying spaces (or moduli stacks) — not necessarily infinite-loop spaces — from which perspective the character map is really an incarnation of the fundamental theorem of rational homotopy theory, thereby not only uniformly subsuming the classical Chern character and a multitude of scattered variants that have been proposed, but now seamlessly applicable in the hitherto elusive generality of (twisted, differential, and) non-abelian cohomology.In laying out this result with plenty of examples, this book provides a modernized introduction and review of fundamental classical topics: 1. abstract homotopy theory via model categories; 2. generalized cohomology in its homotopical incarnation; 3. rational homotopy theory seen via homotopy Lie theory, whose fundamental theorem we recast as a (twisted) non-abelian de Rham theorem, which naturally induces the (twisted) non-abelian character map.