Gauge Symmetries and Fibre Bundles PDF Download
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Author: A.P. Balachandran
Publisher: Springer
ISBN:
Category : Science
Languages : en
Pages : 156
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Book Description
Author: A.P. Balachandran
Publisher: Springer
ISBN:
Category : Science
Languages : en
Pages : 156
Get Book Here
Book Description
Author: A. P. Balachandran
Publisher:
ISBN:
Category :
Languages : en
Pages : 140
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Book Description
Author: David J. Eck
Publisher: American Mathematical Soc.
ISBN: 0821822470
Category : Fiber bundles
Languages : en
Pages : 57
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Book Description
The concept of gauge-natural bundles is introduced. They are a generalization of natural bundles and they provide a natural formal context for the discussion of gauge field theories. It is shown that such bundles correspond to actions of certain Lie groups on smooth manifolds and that natural differential operators between them correspond to equivariant maps. Some results of classical gauge theory are reformulated and reproved in the language of gauge-natural bundles, including a theorem of Utiyama which describes first order gauge-invariant Lagrangians on the bundle of connections of a principal bundle.
Author: Peter W. Michor
Publisher: Amer Inst of Physics
ISBN: 9788870882476
Category : Science
Languages : en
Pages : 107
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Book Description
Author: Jakob Schwichtenberg
Publisher: No-Nonsense Books
ISBN:
Category : Science
Languages : en
Pages : 195
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Book Description
Understanding modern physics doesn’t have to be confusing and hard What if there was an intuitive way to understand how nature fundamentally works? What if there was a book that allowed you to see the whole picture and not just tiny parts of it? Thoughts like this are the reason that Physics from Finance now exists. What will you learn from this book? Get to know all fundamental interactions —Grasp how we can describe electromagnetic interactions, weak interactions, strong interactions and gravity using the same key ideas.Learn how to describe modern physics mathematically — Understand the meaning and origin of the Einstein equation, Maxwell’s equations, and the Schrödinger equation.Develop an intuitive understanding of key concepts — Read how we can understand abstract ideas like Gauge Symmetry, Internal Spaces, Gauge Fields, Connections and Curvature using a simple toy model of the financial market.Get an understanding you can be proud of — Learn why fiber bundles and group theory provide a unified framework for all modern theories of physics. Physics from Finance is the most reader-friendly book on the geometry of modern physics ever written. Here’s why. First of all, it's is nothing like a formal university lecture. Instead, it’s like a casual conservation with a more experienced student. This also means that nothing is assumed to be “obvious” or “easy to see”.Each chapter, each section, and each page focusses solely on the goal to help you understand. Nothing is introduced without a thorough motivation and it is always clear where each formula comes from.The book contains no fluff since unnecessary content quickly leads to confusion. Instead, it ruthlessly focusses on the fundamentals and makes sure you’ll understand them in detail. The primary focus on the readers’ needs is also visible in dozens of small features that you won’t find in any other textbook In total, the book contains more than 100 illustrations that help you understand the most important concepts visually.Whenever a concept is used which was already introduced previously, there is a short sidenote that reminds you where it was first introduced and often recites the main points. In addition, helpful diagrams make sure you won’t get lost.
Author: W. Drechsler
Publisher: Springer
ISBN:
Category : Mathematics
Languages : en
Pages : 262
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Book Description
Author: Wolfgang Drechsler
Publisher:
ISBN:
Category :
Languages : en
Pages : 102
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Book Description
Author: Mark J.D. Hamilton
Publisher: Springer
ISBN: 3319684396
Category : Mathematics
Languages : en
Pages : 667
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Book Description
The Standard Model is the foundation of modern particle and high energy physics. This book explains the mathematical background behind the Standard Model, translating ideas from physics into a mathematical language and vice versa. The first part of the book covers the mathematical theory of Lie groups and Lie algebras, fibre bundles, connections, curvature and spinors. The second part then gives a detailed exposition of how these concepts are applied in physics, concerning topics such as the Lagrangians of gauge and matter fields, spontaneous symmetry breaking, the Higgs boson and mass generation of gauge bosons and fermions. The book also contains a chapter on advanced and modern topics in particle physics, such as neutrino masses, CP violation and Grand Unification. This carefully written textbook is aimed at graduate students of mathematics and physics. It contains numerous examples and more than 150 exercises, making it suitable for self-study and use alongside lecture courses. Only a basic knowledge of differentiable manifolds and special relativity is required, summarized in the appendix.
Author: Eckehard W. Mielke
Publisher: Springer
ISBN: 3319297341
Category : Science
Languages : en
Pages : 377
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Book Description
This monograph aims to provide a unified, geometrical foundation of gauge theories of elementary particle physics. The underlying geometrical structure is unfolded in a coordinate-free manner via the modern mathematical notions of fibre bundles and exterior forms. Topics such as the dynamics of Yang-Mills theories, instanton solutions and topological invariants are included. By transferring these concepts to local space-time symmetries, generalizations of Einstein's theory of gravity arise in a Riemann-Cartan space with curvature and torsion. It provides the framework in which the (broken) Poincaré gauge theory, the Rainich geometrization of the Einstein-Maxwell system, and higher-dimensional, non-abelian Kaluza-Klein theories are developed. Since the discovery of the Higgs boson, concepts of spontaneous symmetry breaking in gravity have come again into focus, and, in this revised edition, these will be exposed in geometric terms. Quantizing gravity remains an open issue: formulating it as a de Sitter type gauge theory in the spirit of Yang-Mills, some new progress in its topological form is presented. After symmetry breaking, Einstein’s standard general relativity with cosmological constant emerges as a classical background. The geometrical structure of BRST quantization with non-propagating topological ghosts is developed in some detail.
Author: David Bleecker
Publisher: Courier Corporation
ISBN: 0486151875
Category : Science
Languages : en
Pages : 202
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Book Description
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.
