Gauge Mechanics

Gauge Mechanics
Title Gauge Mechanics PDF eBook
Author L. Mangiarotti
Publisher World Scientific
Pages 376
Release 1998
Genre Science
ISBN 9789810236038

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This book presents in a unified way modern geometric methods in analytical mechanics based on the application of fibre bundles, jet manifold formalism and the related concept of connection. Non-relativistic mechanics is seen as a particular field theory over a one-dimensional base. In fact, the concept of connection is the major link throughout the book. In the gauge scheme of mechanics, connections appear as reference frames, dynamic equations, and in Lagrangian and Hamiltonian formalisms. Non-inertial forces, energy conservation laws and other phenomena related to reference frames are analyzed; that leads us to observable physics. The gauge formulation of classical mechanics is extended to quantum mechanics under different reference frames. Special topics on geometric BRST mechanics, relativistic mechanics and others, together with many examples, are also dealt with.

Hamiltonian Mechanics of Gauge Systems

Hamiltonian Mechanics of Gauge Systems
Title Hamiltonian Mechanics of Gauge Systems PDF eBook
Author Lev V. Prokhorov
Publisher Cambridge University Press
Pages 485
Release 2011-09-22
Genre Science
ISBN 1139500902

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The principles of gauge symmetry and quantization are fundamental to modern understanding of the laws of electromagnetism, weak and strong subatomic forces and the theory of general relativity. Ideal for graduate students and researchers in theoretical and mathematical physics, this unique book provides a systematic introduction to Hamiltonian mechanics of systems with gauge symmetry. The book reveals how gauge symmetry may lead to a non-trivial geometry of the physical phase space and studies its effect on quantum dynamics by path integral methods. It also covers aspects of Hamiltonian path integral formalism in detail, along with a number of related topics such as the theory of canonical transformations on phase space supermanifolds, non-commutativity of canonical quantization and elimination of non-physical variables. The discussion is accompanied by numerous detailed examples of dynamical models with gauge symmetries, clearly illustrating the key concepts.

Gauge Theories as a Problem of Constructive Quantum Field Theory and Statistical Mechanics

Gauge Theories as a Problem of Constructive Quantum Field Theory and Statistical Mechanics
Title Gauge Theories as a Problem of Constructive Quantum Field Theory and Statistical Mechanics PDF eBook
Author Erhard Seiler
Publisher Springer
Pages 212
Release 1982
Genre Science
ISBN

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Gauge Theory and Variational Principles

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

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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.

Gauge Fields and Strings

Gauge Fields and Strings
Title Gauge Fields and Strings PDF eBook
Author Polyakov
Publisher Routledge
Pages 316
Release 2018-05-02
Genre Mathematics
ISBN 1351446088

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Based on his own work, the author synthesizes the most promising approaches and ideals in field theory today. He presents such subjects as statistical mechanics, quantum field theory and their interrelation, continuous global symmetry, non-Abelian gauge fields, instantons and the quantam theory of loops, and quantum strings and random surfaces. This book is aimed at postgraduate students studying field theory and statistical mechanics, and for research workers in continuous global theory.

The Dawning of Gauge Theory

The Dawning of Gauge Theory
Title The Dawning of Gauge Theory PDF eBook
Author Lochlainn O'Raifeartaigh
Publisher Princeton University Press
Pages
Release 2020-06-30
Genre Science
ISBN 0691215111

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During the course of this century, gauge invariance has slowly emerged from being an incidental symmetry of electromagnetism to being a fundamental geometrical principle underlying the four known fundamental physical interactions. The development has been in two stages. In the first stage (1916-1956) the geometrical significance of gauge-invariance gradually came to be appreciated and the original abelian gauge-invariance of electromagnetism was generalized to non-abelian gauge invariance. In the second stage (1960-1975) it was found that, contrary to first appearances, the non-abelian gauge-theories provided exactly the framework that was needed to describe the nuclear interactions (both weak and strong) and thus provided a universal framework for describing all known fundamental interactions. In this work, Lochlainn O'Raifeartaigh describes the former phase. O'Raifeartaigh first illustrates how gravitational theory and quantum mechanics played crucial roles in the reassessment of gauge theory as a geometric principle and as a framework for describing both electromagnetism and gravitation. He then describes how the abelian electromagnetic gauge-theory was generalized to its present non-abelian form. The development is illustrated by including a selection of relevant articles, many of them appearing here for the first time in English, notably by Weyl, Schrodinger, Klein, and London in the pre-war years, and by Pauli, Shaw, Yang-Mills, and Utiyama after the war. The articles illustrate that the reassessment of gauge-theory, due in a large measure to Weyl, constituted a major philosophical as well as technical advance.

Group Structure of Gauge Theories

Group Structure of Gauge Theories
Title Group Structure of Gauge Theories PDF eBook
Author L. O'Raifeartaigh
Publisher Cambridge University Press
Pages 188
Release 1986
Genre Science
ISBN 9780521347853

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The first portion of the text is devoted to a review of those aspects of Lie groups necessary for the application of group theory to the physics of particles and fields. The second describes the way in which compact Lie groups are used to construct gauge theories.