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The Resource Covariance and gauge invariance in Continuum Physics : application to mechanics, gravitation, and electromagnetism, Lalaonirina R. Rakotomanana

Covariance and gauge invariance in Continuum Physics : application to mechanics, gravitation, and electromagnetism, Lalaonirina R. Rakotomanana

Label
Covariance and gauge invariance in Continuum Physics : application to mechanics, gravitation, and electromagnetism
Title
Covariance and gauge invariance in Continuum Physics
Title remainder
application to mechanics, gravitation, and electromagnetism
Statement of responsibility
Lalaonirina R. Rakotomanana
Creator
Author
Subject
Language
eng
Member of
Cataloging source
N$T
http://library.link/vocab/creatorName
Rakotomanana, Lalao
Dewey number
530.14
Index
no index present
LC call number
QC173.7
Literary form
non fiction
Nature of contents
  • dictionaries
  • bibliography
Series statement
Progress in mathematical physics,
Series volume
volume 73
http://library.link/vocab/subjectName
  • Field theory (Physics)
  • Analysis of covariance
  • Gauge invariance
Label
Covariance and gauge invariance in Continuum Physics : application to mechanics, gravitation, and electromagnetism, Lalaonirina R. Rakotomanana
Instantiates
Publication
Copyright
Antecedent source
unknown
Bibliography note
Includes bibliographical references and index
Carrier category
online resource
Carrier category code
cr
Carrier MARC source
rdacarrier
Color
multicolored
Content category
text
Content type code
txt
Content type MARC source
rdacontent
Contents
  • Intro; Preface; Contents; 1 General Introduction; 1.1 Classical Physics, Lagrangian, and Invariance; 1.2 General Covariance, Gauge Invariance; 1.3 Objectives and Planning; 2 Basic Concepts on Manifolds, Spacetimes, and Calculusof Variations; 2.1 Introduction; 2.2 Space-Time Background; 2.2.1 Basics on Flat Minkowski Spacetime; 2.2.2 Twisted and Curved Spacetimes; 2.3 Manifolds, Tensor Fields, and Connections; 2.3.1 Coordinate System, and Group of Transformations; 2.3.1.1 Manifolds, Tangent Space, Cotangent Space; 2.3.1.2 Change of Coordinate System
  • 2.3.1.3 Examples of Group of Transformations2.3.1.4 Lorentz Invariance; 2.3.2 Elements on Spacetime and Invariance for Relativity; 2.3.2.1 Forms, Tensors and (Pseudo)-Riemannian Manifolds; 2.3.2.2 Hilbert's Causality Principle; 2.3.2.3 Euclidean Spacetime and Isometries; 2.3.2.4 Minkowski Spacetime and Lorentz Transformations; 2.3.2.5 Global Poincaré Transformations; 2.3.3 Volume-Form; 2.3.4 Affine Connection; 2.3.4.1 Affine Connection, Affinely Connected Manifold; 2.3.4.2 Example: Spherical Coordinate System; 2.3.4.3 Example: Elliptic-Hyperbolic Coordinate System
  • 2.3.4.4 Practical Formula for Covariant Derivative2.3.4.5 Torsion and Curvature; 2.3.4.6 Newtonian Spacetime; 2.3.4.7 Levi-Civita Connection; 2.3.4.8 Normal Coordinate System and Inertial Frame; 2.3.5 Tetrads and Affine Connection: Continuum Transformations; 2.3.5.1 Transformation of a Continuum; 2.3.5.2 Holonomic Mapping; 2.3.5.3 Nonholonomic Mapping and Torsion e.g. (2000); 2.3.5.4 Nonholonomic Transformation and Curvature; 2.3.5.5 Torsion, Curvature, and Smoothness of Tensor Fields; 2.4 Invariance for Lagrangian and Euler-Lagrange Equations
  • 2.4.1 Covariant Formulation of Classical Mechanics of a Particle2.4.2 Basic Elements for Calculus of Variations; 2.4.3 Extended Euler-Lagrange Equations; 2.5 Simple Examples in Continuum and Relativistic Mechanics; 2.5.1 Particles in a Minkowski Spacetime; 2.5.2 Some Continua Examples; 2.5.2.1 Energy-Momentum Tensor; 2.5.2.2 Dust in Relativistic Mechanics; 2.5.2.3 Perfect Fluids in Relativistic Mechanics; 2.5.2.4 Strain Gradient Continuum; 3 Covariance of Lagrangian Density Function; 3.1 Introduction; 3.2 Some Basic Theorems; 3.2.1 Theorem of Cartan; 3.2.2 Theorem of lovelockarma
  • 3.2.3 Theorem of Quotient3.3 Invariance with Respect to the Metric; 3.3.1 Transformation Rules for the Metric and Its Derivatives; 3.3.2 Introduction of Dual Variables; 3.3.3 Theorem; 3.4 Invariance with Respect to the Connection; 3.4.1 Preliminary; 3.4.2 Application: Covariance of L; 3.4.3 Summary for Lagrangian Covariance; 3.4.4 Covariance of Nonlinear Elastic Continuum; 3.4.4.1 Covariance of Strain Energy Density; 3.4.4.2 Examples of Nonlinear Elastic Material Models; 4 Gauge Invariance for Gravitation and Gradient Continuum; 4.1 Introduction to Gauge Invariance
Dimensions
unknown
Extent
1 online resource.
File format
unknown
Form of item
online
Isbn
9783319917818
Level of compression
unknown
Media category
computer
Media MARC source
rdamedia
Media type code
c
Quality assurance targets
not applicable
Reformatting quality
unknown
Sound
unknown sound
Specific material designation
remote
System control number
  • on1043831002
  • (OCoLC)1043831002
Label
Covariance and gauge invariance in Continuum Physics : application to mechanics, gravitation, and electromagnetism, Lalaonirina R. Rakotomanana
Publication
Copyright
Antecedent source
unknown
Bibliography note
Includes bibliographical references and index
Carrier category
online resource
Carrier category code
cr
Carrier MARC source
rdacarrier
Color
multicolored
Content category
text
Content type code
txt
Content type MARC source
rdacontent
Contents
  • Intro; Preface; Contents; 1 General Introduction; 1.1 Classical Physics, Lagrangian, and Invariance; 1.2 General Covariance, Gauge Invariance; 1.3 Objectives and Planning; 2 Basic Concepts on Manifolds, Spacetimes, and Calculusof Variations; 2.1 Introduction; 2.2 Space-Time Background; 2.2.1 Basics on Flat Minkowski Spacetime; 2.2.2 Twisted and Curved Spacetimes; 2.3 Manifolds, Tensor Fields, and Connections; 2.3.1 Coordinate System, and Group of Transformations; 2.3.1.1 Manifolds, Tangent Space, Cotangent Space; 2.3.1.2 Change of Coordinate System
  • 2.3.1.3 Examples of Group of Transformations2.3.1.4 Lorentz Invariance; 2.3.2 Elements on Spacetime and Invariance for Relativity; 2.3.2.1 Forms, Tensors and (Pseudo)-Riemannian Manifolds; 2.3.2.2 Hilbert's Causality Principle; 2.3.2.3 Euclidean Spacetime and Isometries; 2.3.2.4 Minkowski Spacetime and Lorentz Transformations; 2.3.2.5 Global Poincaré Transformations; 2.3.3 Volume-Form; 2.3.4 Affine Connection; 2.3.4.1 Affine Connection, Affinely Connected Manifold; 2.3.4.2 Example: Spherical Coordinate System; 2.3.4.3 Example: Elliptic-Hyperbolic Coordinate System
  • 2.3.4.4 Practical Formula for Covariant Derivative2.3.4.5 Torsion and Curvature; 2.3.4.6 Newtonian Spacetime; 2.3.4.7 Levi-Civita Connection; 2.3.4.8 Normal Coordinate System and Inertial Frame; 2.3.5 Tetrads and Affine Connection: Continuum Transformations; 2.3.5.1 Transformation of a Continuum; 2.3.5.2 Holonomic Mapping; 2.3.5.3 Nonholonomic Mapping and Torsion e.g. (2000); 2.3.5.4 Nonholonomic Transformation and Curvature; 2.3.5.5 Torsion, Curvature, and Smoothness of Tensor Fields; 2.4 Invariance for Lagrangian and Euler-Lagrange Equations
  • 2.4.1 Covariant Formulation of Classical Mechanics of a Particle2.4.2 Basic Elements for Calculus of Variations; 2.4.3 Extended Euler-Lagrange Equations; 2.5 Simple Examples in Continuum and Relativistic Mechanics; 2.5.1 Particles in a Minkowski Spacetime; 2.5.2 Some Continua Examples; 2.5.2.1 Energy-Momentum Tensor; 2.5.2.2 Dust in Relativistic Mechanics; 2.5.2.3 Perfect Fluids in Relativistic Mechanics; 2.5.2.4 Strain Gradient Continuum; 3 Covariance of Lagrangian Density Function; 3.1 Introduction; 3.2 Some Basic Theorems; 3.2.1 Theorem of Cartan; 3.2.2 Theorem of lovelockarma
  • 3.2.3 Theorem of Quotient3.3 Invariance with Respect to the Metric; 3.3.1 Transformation Rules for the Metric and Its Derivatives; 3.3.2 Introduction of Dual Variables; 3.3.3 Theorem; 3.4 Invariance with Respect to the Connection; 3.4.1 Preliminary; 3.4.2 Application: Covariance of L; 3.4.3 Summary for Lagrangian Covariance; 3.4.4 Covariance of Nonlinear Elastic Continuum; 3.4.4.1 Covariance of Strain Energy Density; 3.4.4.2 Examples of Nonlinear Elastic Material Models; 4 Gauge Invariance for Gravitation and Gradient Continuum; 4.1 Introduction to Gauge Invariance
Dimensions
unknown
Extent
1 online resource.
File format
unknown
Form of item
online
Isbn
9783319917818
Level of compression
unknown
Media category
computer
Media MARC source
rdamedia
Media type code
c
Quality assurance targets
not applicable
Reformatting quality
unknown
Sound
unknown sound
Specific material designation
remote
System control number
  • on1043831002
  • (OCoLC)1043831002

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