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Gauge Theory and Variational Principles

Gauge Theory and Variational Principles Author David Bleecker
ISBN-10 9780486151878
Release 2013-01-18
Pages 208
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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



Variational Principles

Variational Principles Author B. L. Moiseiwitsch
ISBN-10 9780486150499
Release 2013-02-20
Pages 320
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This text shows how variational principles are used to determine the discrete eigenvalues for stationary state problems and to illustrate how to find the values of quantities that arise in the theory of scattering. 1966 edition.



Variational Principles in Dynamics and Quantum Theory

Variational Principles in Dynamics and Quantum Theory Author Wolfgang Yourgrau
ISBN-10 9780486151137
Release 2012-04-26
Pages 224
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DIVHistorical, theoretical survey with many insights, much hard-to-find material. Hamilton’s principle, Hamilton-Jacobi equation, etc. /div



Tensors Differential Forms and Variational Principles

Tensors  Differential Forms  and Variational Principles Author David Lovelock
ISBN-10 9780486131986
Release 2012-04-20
Pages 400
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Incisive, self-contained account of tensor analysis and the calculus of exterior differential forms, interaction between the concept of invariance and the calculus of variations. Emphasis is on analytical techniques. Includes problems.



The Variational Principles of Mechanics

The Variational Principles of Mechanics Author Cornelius Lanczos
ISBN-10 9780486134703
Release 2012-04-24
Pages 464
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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.



Mathematical Gauge Theory

Mathematical Gauge Theory Author Mark J.D. Hamilton
ISBN-10 9783319684390
Release 2017-12-06
Pages 658
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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.



The Dawning of Gauge Theory

The Dawning of Gauge Theory Author Lochlainn O'Raifeartaigh
ISBN-10 0691029776
Release 1997
Pages 249
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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.



An Invitation to Quantum Field Theory

An Invitation to Quantum Field Theory Author Luis Alvarez-Gaumé
ISBN-10 9783642237270
Release 2011-11-26
Pages 294
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This book provides an introduction to Quantum Field Theory (QFT) at an elementary level—with only special relativity, electromagnetism and quantum mechanics as prerequisites. For this fresh approach to teaching QFT, based on numerous lectures and courses given by the authors, a representative sample of topics has been selected containing some of the more innovative, challenging or subtle concepts. They are presented with a minimum of technical details, the discussion of the main ideas being more important than the presentation of the typically very technical mathematical details necessary to obtain the final results. Special attention is given to the realization of symmetries in particle physics: global and local symmetries, explicit, spontaneously broken, and anomalous continuous symmetries, as well as discrete symmetries. Beyond providing an overview of the standard model of the strong, weak and electromagnetic interactions and the current understanding of the origin of mass, the text enumerates the general features of renormalization theory as well as providing a cursory description of effective field theories and the problem of naturalness in physics. Among the more advanced topics the reader will find are an outline of the first principles derivation of the CPT theorem and the spin-statistics connection. As indicated by the title, the main aim of this text is to motivate the reader to study QFT by providing a self-contained and approachable introduction to the most exciting and challenging aspects of this successful theoretical framework.



Electrodynamics and Classical Theory of Fields and Particles

Electrodynamics and Classical Theory of Fields and Particles Author A. O. Barut
ISBN-10 9780486158716
Release 2012-04-30
Pages 256
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Comprehensive graduate-level text by a distinguished theoretical physicist reveals the classical underpinnings of modern quantum field theory. Topics include space-time, Lorentz transformations, conservation laws, equations of motion, Green’s functions, and more. 1964 edition.



Classical Field Theory

Classical Field Theory Author Davison E. Soper
ISBN-10 9780486462608
Release 2008-02-04
Pages 272
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This text concerns continuum mechanics, electrodynamics and the mechanics of electrically polarized media, and gravity. Geared toward advanced undergraduates and graduate students, it offers an accessible approach that formulates theories according to the principle of least action. The chief advantage of this formulation is its simplicity and ease, making the physical content of classical subjects available to students of physics in a concise form. Author Davison E. Soper, a Professor of Physics at the University of Oregon, intended this treatment as a primary text for courses in classical field theory as well as a supplement for courses in classical mechanics or classical electrodynamics. Topics include fields and transformation laws, the principle of stationary action, general features of classical field theory, the mechanics of fluids and elastic solids, special types of solids, nonrelativistic approximations, and the electromagnetic field. Additional subjects include electromagnetically polarized materials, gravity, momentum conservation in general relativity, and dissipative processes.



Geometrical Methods of Mathematical Physics

Geometrical Methods of Mathematical Physics Author Bernard F. Schutz
ISBN-10 9781107268142
Release 1980-01-28
Pages
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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.



Partial Differential Equations of Mathematical Physics

Partial Differential Equations of Mathematical Physics Author S. L. Sobolev
ISBN-10 048665964X
Release 1964
Pages 427
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This volume presents an unusually accessible introduction to equations fundamental to the investigation of waves, heat conduction, hydrodynamics, and other physical problems. Topics include derivation of fundamental equations, Riemann method, equation of heat conduction, theory of integral equations, Green's function, and much more. The only prerequisite is a familiarity with elementary analysis. 1964 edition.



Differential Geometry

Differential Geometry Author Erwin Kreyszig
ISBN-10 9780486318622
Release 2013-04-26
Pages 384
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An introductory textbook on the differential geometry of curves and surfaces in 3-dimensional Euclidean space, presented in its simplest, most essential form. With problems and solutions. Includes 99 illustrations.



Calculus of Variations

Calculus of Variations Author Robert Weinstock
ISBN-10 0486630692
Release 1974
Pages 326
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This text is basically divided into two parts. Chapters 1–4 include background material, basic theorems and isoperimetric problems. Chapters 5–12 are devoted to applications, geometrical optics, particle dynamics, the theory of elasticity, electrostatics, quantum mechanics, and other topics. Exercises in each chapter. 1952 edition.



The Functions of Mathematical Physics

The Functions of Mathematical Physics Author Harry Hochstadt
ISBN-10 9780486168784
Release 2012-04-30
Pages 352
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Comprehensive text provides a detailed treatment of orthogonal polynomials, principal properties of the gamma function, hypergeometric functions, Legendre functions, confluent hypergeometric functions, and Hill's equation.



Differential Calculus and Its Applications

Differential Calculus and Its Applications Author Michael J. Field
ISBN-10 9780486298849
Release 2013-04-10
Pages 336
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Based on undergraduate courses in advanced calculus, the treatment covers a wide range of topics, from soft functional analysis and finite-dimensional linear algebra to differential equations on submanifolds of Euclidean space. 1976 edition.



An Introduction to the Calculus of Variations

An Introduction to the Calculus of Variations Author Charles Fox
ISBN-10 0486654990
Release 1950
Pages 271
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In this highly regarded text for advanced undergraduate and graduate students, the author develops the calculus of variations both for its intrinsic interest and for its powerful applications to modern mathematical physics. Topics include first and second variations of an integral, generalizations, isoperimetrical problems, least action, special relativity, elasticity, more. 1963 edition.