# gauge theory and variational principles dover books on mathematics

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## Gauge Theory And Variational Principles

**Author :**David Bleecker

**ISBN :**9780486151878

**Genre :**Science

**File Size :**76. 99 MB

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Covers principal fiber bundles and connections; curvature; particle fields, Lagrangians, and gauge invariance; inhomogeneous field equations; free Dirac electron fields; calculus on frame bundle; and unification of gauge fields and gravitation. 1981 edition

## Differential Geometry Gauge Theories And Gravity

**Author :**M. Göckeler

**ISBN :**0521378214

**Genre :**Mathematics

**File Size :**85. 54 MB

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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.

## The Dawning Of Gauge Theory

**Author :**Lochlainn O'Raifeartaigh

**ISBN :**0691029776

**Genre :**Science

**File Size :**31. 33 MB

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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.

## Geometrical Methods Of Mathematical Physics

**Author :**Bernard F. Schutz

**ISBN :**9781107268142

**Genre :**Science

**File Size :**84. 14 MB

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In recent years the methods of modern differential geometry have become of considerable importance in theoretical physics and have found application in relativity and cosmology, high-energy physics and field theory, thermodynamics, fluid dynamics and mechanics. This textbook provides an introduction to these methods - in particular Lie derivatives, Lie groups and differential forms - and covers their extensive applications to theoretical physics. The reader is assumed to have some familiarity with advanced calculus, linear algebra and a little elementary operator theory. The advanced physics undergraduate should therefore find the presentation quite accessible. This account will prove valuable for those with backgrounds in physics and applied mathematics who desire an introduction to the subject. Having studied the book, the reader will be able to comprehend research papers that use this mathematics and follow more advanced pure-mathematical expositions.

## Variational Principles In Dynamics And Quantum Theory

**Author :**Wolfgang Yourgrau

**ISBN :**9780486151137

**Genre :**Science

**File Size :**38. 29 MB

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DIVHistorical, theoretical survey with many insights, much hard-to-find material. Hamilton’s principle, Hamilton-Jacobi equation, etc. /div

## The Variational Principles Of Mechanics

**Author :**Cornelius Lanczos

**ISBN :**9780486134703

**Genre :**Science

**File Size :**47. 54 MB

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Philosophic, less formalistic approach to analytical mechanics offers model of clear, scholarly exposition at graduate level with coverage of basics, calculus of variations, principle of virtual work, equations of motion, more.

## Partial Differential Equations And Group Theory

**Author :**J.F. Pommaret

**ISBN :**9789401725392

**Genre :**Mathematics

**File Size :**38. 92 MB

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Ordinary differential control thPory (the classical theory) studies input/output re lations defined by systems of ordinary differential equations (ODE). The various con cepts that can be introduced (controllability, observability, invertibility, etc. ) must be tested on formal objects (matrices, vector fields, etc. ) by means of formal operations (multiplication, bracket, rank, etc. ), but without appealing to the explicit integration (search for trajectories, etc. ) of the given ODE. Many partial results have been re cently unified by means of new formal methods coming from differential geometry and differential algebra. However, certain problems (invariance, equivalence, linearization, etc. ) naturally lead to systems of partial differential equations (PDE). More generally, partial differential control theory studies input/output relations defined by systems of PDE (mechanics, thermodynamics, hydrodynamics, plasma physics, robotics, etc. ). One of the aims of this book is to extend the preceding con cepts to this new situation, where, of course, functional analysis and/or a dynamical system approach cannot be used. A link will be exhibited between this domain of applied mathematics and the famous 'Backlund problem', existing in the study of solitary waves or solitons. In particular, we shall show how the methods of differ ential elimination presented here will allow us to determine compatibility conditions on input and/or output as a better understanding of the foundations of control the ory. At the same time we shall unify differential geometry and differential algebra in a new framework, called differential algebraic geometry.

## Variational Principles

**Author :**B. L. Moiseiwitsch

**ISBN :**9780486438177

**Genre :**Mathematics

**File Size :**28. 39 MB

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This graduate-level text's primary objective is to demonstrate the expression of the equations of the various branches of mathematical physics in the succinct and elegant form of variational principles (and thereby illuminate their interrelationship). Its related intentions are to show how variational principles may be employed to determine the discrete eigenvalues for stationary state problems and to illustrate how to find the values of quantities (such as the phase shifts) that arise in the theory of scattering. Chapter-by-chapter treatment consists of analytical dynamics; optics, wave mechanics, and quantum mechanics; field equations; eigenvalue problems; and scattering theory. 1966 edition. Bibliography. Index.

## Tensors And Manifolds

**Author :**Robert Wasserman

**ISBN :**0198510594

**Genre :**Foreign Language Study

**File Size :**66. 83 MB

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The book sets forth the basic principles of tensors and manifolds, describing how the mathematics underlies elegant geometrical models of classical mechanics, relativity and elementary particle physics."--Jacket.

## Classical Mechanics

**Author :**J. Michael Finn

**ISBN :**9780763779603

**Genre :**Science

**File Size :**58. 45 MB

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Classical Mechanics presents an updated treatment of the dynamics of particles and particle systems suitable for students preparing for advanced study of physics and closely related fields, such as astronomy and the applied engineering sciences. Compared to older books on this subject, the mathematical treatment has been updated for the study of more advanced topics in quantum mechanics, statistical mechanics, and nonlinear and orbital mechanics. The text begins with a review of the principles of classical Newtonian dynamics of particles and particle systems and proceeds to show how these principles are modified and extended by developments in the field. The text ends with the unification of space and time given by the Special Theory of Relativity. In addition, Hamiltonian dynamics and the concept of phase space are introduced early on. This allows integration of the concepts of chaos and other nonlinear effects into the main flow of the text. The role of symmetries and the underlying geometric structure of space-time is a key theme. In the latter chapters, the connection between classical and quantum mechanics is examined in some detail.