Differential Geometry, Gauge Theories, and Gravity

Differential Geometry, Gauge Theories, and Gravity
Author: M. Göckeler
Publisher: Cambridge University Press
Total Pages: 248
Release: 1989-07-28
Genre: Mathematics
ISBN: 9780521378215

Cambridge University Press is committed to keeping scholarly work in print for as long as possible. A short print-run of this academic paperback has been produced using digital technology. This technology has enabled Cambridge to keep the book in print for specialists and students when traditional methods of reprinting would not have been feasible. While the new digital cover differs from the original, the text content is identical to that of previous printings.

Modern Differential Geometry in Gauge Theories

Modern Differential Geometry in Gauge Theories
Author: Anastasios Mallios
Publisher: Springer Science & Business Media
Total Pages: 303
Release: 2006-07-27
Genre: Mathematics
ISBN: 0817644741

This is original, well-written work of interest Presents for the first time (physical) field theories written in sheaf-theoretic language Contains a wealth of minutely detailed, rigorous computations, ususally absent from standard physical treatments Author's mastery of the subject and the rigorous treatment of this text make it invaluable

Gauge Theories and Differential Geometry

Gauge Theories and Differential Geometry
Author: Lance Bailey
Publisher: Nova Science Publishers
Total Pages: 0
Release: 2016
Genre: Gauge fields (Physics)
ISBN: 9781634835466

This book revisits the mathematical foundations of thermodynamics and gauge theory by using new differential geometric methods coming from the formal theory of systems of partial differential equations and Lie pseudogroups. The gauge theory of gravity is also established, in which spinorial and ventorial matter fields serve as gravitating sources. The potential applications of the present gauge theory of gravity, including quantum-vacuum-energy gravity, cosmological constant problem and gravity-gauge unification is also addressed. The third chapter focuses on a gravitational gauge theory with spin connection and vierbein as fundamental variables of gravity. Next, the place and physical significance of Poincaré gauge theory of gravity (PGTG) in the framework of gauge approach to gravitation is discussed. A cutoff regularization method in gauge theory is discussed in Chapter Five. The remaining chapters in the book focus on differential geometry, in particular, the authors show how fractional differential derived from fractional difference provides a basis to expand a theory of fractional differential geometry which would apply to non-differentiable manifolds; a review of the infinitesimal Baker-Campbell-Hausdorff formula is provided and the book concludes with a short communication where the authors focus on local stability, and describe how this leads naturally into the question of finite-time singularities and generalized soliton solutions.

Gauge Theory and Variational Principles

Gauge Theory and Variational Principles
Author: David Bleecker
Publisher: Courier Corporation
Total Pages: 202
Release: 2005-12-10
Genre: Science
ISBN: 0486445461

This text provides a framework for describing and organizing the basic forces of nature and the interactions of subatomic particles. A detailed and self-contained mathematical account of gauge theory, it is geared toward beginning graduate students and advanced undergraduates in mathematics and physics. This well-organized treatment supplements its rigor with intuitive ideas. Starting with an examination of principal fiber bundles and connections, the text explores curvature; particle fields, Lagrangians, and gauge invariance; Lagrange's equation for particle fields; and the inhomogeneous field equation. Additional topics include free Dirac electron fields; interactions; calculus on frame bundle; and unification of gauge fields and gravitation. The text concludes with references, a selected bibliography, an index of notation, and a general index.

Loops, Knots, Gauge Theories

Loops, Knots, Gauge Theories
Author: Rodolfo Gambini
Publisher: Cambridge University Press
Total Pages: 341
Release: 2023-01-31
Genre: Science
ISBN: 1009290193

This volume provides a self-contained introduction to applications of loop representations in particle physics and quantum gravity, in order to explore the gauge invariant quantization of Yang-Mills theories and gravity. First published in 1996, this title has been reissued as an Open Access publication on Cambridge Core.

Gauge Fields, Knots, and Gravity

Gauge Fields, Knots, and Gravity
Author: Associate Professor Department of Mathematics John C Baez
Publisher: World Scientific Publishing Company Incorporated
Total Pages: 465
Release: 1994
Genre: Science
ISBN: 9789810217297

This is an introduction to the basic tools of mathematics needed to understand the relation between knot theory and quantum gravity. The book begins with a rapid course on manifolds and differential forms, emphasizing how these provide a proper language for formulating Maxwell's equations on arbitrary spacetimes. The authors then introduce vector bundles, connections and curvature in order to generalize Maxwell theory to the Yang-Mills equations. The relation of gauge theory to the newly discovered knot invariants such as the Jones polynomial is sketched. Riemannian geometry is then introduced in order to describe Einstein's equations of general relativity and show how an attempt to quantize gravity leads to interesting applications of knot theory.

Differential Geometry and Mathematical Physics

Differential Geometry and Mathematical Physics
Author: Gerd Rudolph
Publisher: Springer Science & Business Media
Total Pages: 766
Release: 2012-11-09
Genre: Science
ISBN: 9400753454

Starting from an undergraduate level, this book systematically develops the basics of • Calculus on manifolds, vector bundles, vector fields and differential forms, • Lie groups and Lie group actions, • Linear symplectic algebra and symplectic geometry, • Hamiltonian systems, symmetries and reduction, integrable systems and Hamilton-Jacobi theory. The topics listed under the first item are relevant for virtually all areas of mathematical physics. The second and third items constitute the link between abstract calculus and the theory of Hamiltonian systems. The last item provides an introduction to various aspects of this theory, including Morse families, the Maslov class and caustics. The book guides the reader from elementary differential geometry to advanced topics in the theory of Hamiltonian systems with the aim of making current research literature accessible. The style is that of a mathematical textbook,with full proofs given in the text or as exercises. The material is illustrated by numerous detailed examples, some of which are taken up several times for demonstrating how the methods evolve and interact.

Gauge/Gravity Duality

Gauge/Gravity Duality
Author: Martin Ammon
Publisher: Cambridge University Press
Total Pages: 549
Release: 2015-04-09
Genre: Juvenile Nonfiction
ISBN: 1107010349

The first textbook on this important topic, for graduate students and researchers in particle and condensed matter physics.

Differential Geometry and Lie Groups for Physicists

Differential Geometry and Lie Groups for Physicists
Author: Marián Fecko
Publisher: Cambridge University Press
Total Pages: 11
Release: 2006-10-12
Genre: Science
ISBN: 1139458035

Covering subjects including manifolds, tensor fields, spinors, and differential forms, this textbook introduces geometrical topics useful in modern theoretical physics and mathematics. It develops understanding through over 1000 short exercises, and is suitable for advanced undergraduate or graduate courses in physics, mathematics and engineering.

Supergravity

Supergravity
Author: Daniel Z. Freedman
Publisher: Cambridge University Press
Total Pages: 626
Release: 2012-04-05
Genre: Science
ISBN: 1139642855

Supergravity, together with string theory, is one of the most significant developments in theoretical physics. Written by two of the most respected workers in the field, this is the first-ever authoritative and systematic account of supergravity. The book starts by reviewing aspects of relativistic field theory in Minkowski spacetime. After introducing the relevant ingredients of differential geometry and gravity, some basic supergravity theories (D=4 and D=11) and the main gauge theory tools are explained. In the second half of the book, complex geometry and N=1 and N=2 supergravity theories are covered. Classical solutions and a chapter on AdS/CFT complete the book. Numerous exercises and examples make it ideal for Ph.D. students, and with applications to model building, cosmology and solutions of supergravity theories, it is also invaluable to researchers. A website hosted by the authors, featuring solutions to some exercises and additional reading material, can be found at www.cambridge.org/supergravity.