Applications of Noncommutative Geometry to Gauge Theories, Field Theories, and Quantum Space-Time

Hardcover

Kurzbeschreibung des Verlags

Noncommutative geometry has emerged over the past decades as a powerful conceptual and technical framework for extending the methods of geometry and topology to contexts where the classical notion of space-time, described in terms of smooth manifolds, is no longer adequate. Motivated both by internal developments in mathematics and by profound questions arising in modern theoretical physics, noncommutative geometry provides a unifying language in which algebraic, analytic, and geometric ideas are deeply intertwined. In particular, it offers new perspectives on gauge theories, quantum field theories, and the structure of space-time at the Planck scale, where quantum and gravitational effects are expected to become inseparable.

The central idea of noncommutative geometry is to replace the algebra of functions on a space by a noncommutative algebra, thereby encoding geometric information in purely algebraic and spectral terms. This paradigm shift allows one to generalize notions such as metrics, connections, curvature, and topological invariants to settings far beyond classical geometry. Spectral triples, cyclic cohomology, and operator-algebraic methods play a fundamental role in this approach, providing tools that are well adapted to the analysis of quantum systems and field-theoretic models.

The present volume explores this framework through a series of contributions that address, from complementary viewpoints, the application of noncommutative geometry to gauge theories, quantum field theories, and models of quantum space-time. Each contribution combines mathematical rigor with physical motivation, emphasizing both conceptual clarity and technical depth.

• Reihe: EMS Series of Lectures in Mathematics
• Themen: Mathematik und Naturwissenschaften Mathematik Topologie Analytische Topologie
• ISBN: 9783985471089
• Sprache: Englisch
• Erscheinungsdatum: 01.06.2026
• Größe: 24 x 17 cm
• Verlag: EMS Press
• Herausgegeben von: Ali H. Chamseddine, Alain Connes, Masoud Khalkhali, Joseph Kouneiher