The Resource Group theory and general relativity : representations of the Lorentz group and their applications to the gravitational field, Moshe Carmeli
Group theory and general relativity : representations of the Lorentz group and their applications to the gravitational field, Moshe Carmeli
Resource Information
The item Group theory and general relativity : representations of the Lorentz group and their applications to the gravitational field, Moshe Carmeli represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Missouri-St. Louis Libraries.This item is available to borrow from 1 library branch.
Resource Information
The item Group theory and general relativity : representations of the Lorentz group and their applications to the gravitational field, Moshe Carmeli represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Missouri-St. Louis Libraries.
This item is available to borrow from 1 library branch.
- Summary
- This is the only book on the subject of group theory and Einstein's theory of gravitation. It contains an extensive discussion on general relativity from the viewpoint of group theory and gauge fields. It also puts together in one volume many scattered, original works, on the use of group theory in general relativity theory. There are twelve chapters in the book. The first six are devoted to rotation and Lorentz groups, and their representations. They include the spinor representation as well as the infinite-dimensional representations. The other six chapters deal with the application of groups - particularly the Lorentz and the SL(2, C) groups - to the theory of general relativity. Each chapter is concluded with a set of problems. The topics covered range from the fundamentals of general relativity theory, its formulation as an SL(2, C) gauge theory, to exact solutions of the Einstein gravitational field equations. The important Bondi-Metzner-Sachs group, and its representations, conclude the book. The entire book is self-contained in both group theory and general relativity theory, and no prior knowledge of either is assumed. The subject of this book constitutes a relevant link between field theoreticians and general relativity theoreticians, who usually work rather independently of each other. The treatise is highly topical and of real interest to theoretical physicists, general relativists and applied mathematicians. It is invaluable to graduate students and research workers in quantum field theory, general relativity and elementary particle theory
- Language
- eng
- Extent
- 1 online resource (xviii, 391 pages)
- Note
- Originally published: New York : McGraw-Hill, ©1977
- Contents
-
- 1. The rotation group. 1.1. The three-dimensional pure rotation group. 1.2. The group SU[symbol]. 1.3. Invariant integral over the groups O[symbol] and SU[symbol]. 1.4. Representations of the groups O[symbol] and SU[symbol]. 1.5. Matrix elements of irreducible representations. 1.6. Differential operators of infinitesimal rotations
- 2. The Lorentz group. 2.1. Infinitesimal Lorentz matrices. 2.2. Infinitesimal Operators. 2.3. Representations of the group L
- 3. Spinor representation of the Lorentz group. 3.1. The group SL(2, C) and the Lorentz group. 3.2. Spinor representation of the group SL(2, C). 3.3. Infinitesimal operators of the spinor representation
- 4. Principal series of representations of SL(2, C). 4.1. Linear spaces of representations. 4.2. The group operators. 4.3. SU[symbol] description of the principal series. 4.4. Comparison with the infinitesimal approach
- 5. Complementary series of representations of SL(2, C). 5.1. Realization of the complementary series. 5.2. SU[symbol] description of the complementary series. 5.3. Operator formulation
- 6. Complete series of representations of SL(2, C). 6.1. Realization of the complete series. 6.2. Complete series and spinors. 6.3. Unitary representations case. 6.4. Harmonic analysis on the group SL(2, C)
- 7. Elements of general relativity theory. 7.1. Riemannian geometry. 7.2. Principle of equivalence. 7.3. Principle of general covariance. 7.4. Gravitational field equations. 7.5. Solutions of Einstein's field equations. 7.6. Experimental tests of general relativity. 7.7. Equations of motion
- 8. Spinors in general relativity. 8.1. Connection between spinors and tensors. 8.2. Maxwell, Weyl and Riemann spinors. 8.3. Classification of Maxwell spinor. 8.4. Classification of Weyl spinor
- 9. SL(2, C) gauge theory of the gravitational field: the Newman-Penrose equations. 9.1. Isotopic spin and gauge fields. 9.2. Lorentz invariance and the gravitational field. 9.3. SL(2, C) invariance and the gravitational field. 9.4. Gravitational field equations
- 10. Analysis of the gravitational field. 10.1. Geometrical interpretation. 10.2. Choice of coordinate system. 10.3. Asymptotic behavior
- 11. Some exact solutions of the gravitational field equations. 11.1. Solutions containing hypersurface orthogonal geodesic rays. 11.2. The NUT-Taub metric. 11.3. Type D vacuum metrics
- 12. The Bondi-Metzner-Sachs group. 12.1. The Bondi-Metzner-Sachs group. 12.2. The structure of the Bondi-Metzner-Sachs Group
- Isbn
- 9781848160187
- Label
- Group theory and general relativity : representations of the Lorentz group and their applications to the gravitational field
- Title
- Group theory and general relativity
- Title remainder
- representations of the Lorentz group and their applications to the gravitational field
- Statement of responsibility
- Moshe Carmeli
- Language
- eng
- Summary
- This is the only book on the subject of group theory and Einstein's theory of gravitation. It contains an extensive discussion on general relativity from the viewpoint of group theory and gauge fields. It also puts together in one volume many scattered, original works, on the use of group theory in general relativity theory. There are twelve chapters in the book. The first six are devoted to rotation and Lorentz groups, and their representations. They include the spinor representation as well as the infinite-dimensional representations. The other six chapters deal with the application of groups - particularly the Lorentz and the SL(2, C) groups - to the theory of general relativity. Each chapter is concluded with a set of problems. The topics covered range from the fundamentals of general relativity theory, its formulation as an SL(2, C) gauge theory, to exact solutions of the Einstein gravitational field equations. The important Bondi-Metzner-Sachs group, and its representations, conclude the book. The entire book is self-contained in both group theory and general relativity theory, and no prior knowledge of either is assumed. The subject of this book constitutes a relevant link between field theoreticians and general relativity theoreticians, who usually work rather independently of each other. The treatise is highly topical and of real interest to theoretical physicists, general relativists and applied mathematicians. It is invaluable to graduate students and research workers in quantum field theory, general relativity and elementary particle theory
- Cataloging source
- N$T
- http://library.link/vocab/creatorDate
- 1933-
- http://library.link/vocab/creatorName
- Carmeli, Moshe
- Dewey number
- 530.11/01/5122
- Index
- index present
- LC call number
- QC174.52.L6
- LC item number
- .C37 2000eb
- Literary form
- non fiction
- Nature of contents
-
- dictionaries
- bibliography
- http://library.link/vocab/subjectName
-
- Lorentz transformations
- SCIENCE
- Lorentz transformations
- Darstellung
- Anwendung
- Gravitationsfeld
- Allgemeine Relativitätstheorie
- Gruppentheorie
- Lorentz-Gruppe
- Label
- Group theory and general relativity : representations of the Lorentz group and their applications to the gravitational field, Moshe Carmeli
- Note
- Originally published: New York : McGraw-Hill, ©1977
- Antecedent source
- unknown
- Bibliography note
- Includes bibliographical references (pages 343-375) 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
- 1. The rotation group. 1.1. The three-dimensional pure rotation group. 1.2. The group SU[symbol]. 1.3. Invariant integral over the groups O[symbol] and SU[symbol]. 1.4. Representations of the groups O[symbol] and SU[symbol]. 1.5. Matrix elements of irreducible representations. 1.6. Differential operators of infinitesimal rotations -- 2. The Lorentz group. 2.1. Infinitesimal Lorentz matrices. 2.2. Infinitesimal Operators. 2.3. Representations of the group L -- 3. Spinor representation of the Lorentz group. 3.1. The group SL(2, C) and the Lorentz group. 3.2. Spinor representation of the group SL(2, C). 3.3. Infinitesimal operators of the spinor representation -- 4. Principal series of representations of SL(2, C). 4.1. Linear spaces of representations. 4.2. The group operators. 4.3. SU[symbol] description of the principal series. 4.4. Comparison with the infinitesimal approach -- 5. Complementary series of representations of SL(2, C). 5.1. Realization of the complementary series. 5.2. SU[symbol] description of the complementary series. 5.3. Operator formulation -- 6. Complete series of representations of SL(2, C). 6.1. Realization of the complete series. 6.2. Complete series and spinors. 6.3. Unitary representations case. 6.4. Harmonic analysis on the group SL(2, C) -- 7. Elements of general relativity theory. 7.1. Riemannian geometry. 7.2. Principle of equivalence. 7.3. Principle of general covariance. 7.4. Gravitational field equations. 7.5. Solutions of Einstein's field equations. 7.6. Experimental tests of general relativity. 7.7. Equations of motion -- 8. Spinors in general relativity. 8.1. Connection between spinors and tensors. 8.2. Maxwell, Weyl and Riemann spinors. 8.3. Classification of Maxwell spinor. 8.4. Classification of Weyl spinor -- 9. SL(2, C) gauge theory of the gravitational field: the Newman-Penrose equations. 9.1. Isotopic spin and gauge fields. 9.2. Lorentz invariance and the gravitational field. 9.3. SL(2, C) invariance and the gravitational field. 9.4. Gravitational field equations -- 10. Analysis of the gravitational field. 10.1. Geometrical interpretation. 10.2. Choice of coordinate system. 10.3. Asymptotic behavior -- 11. Some exact solutions of the gravitational field equations. 11.1. Solutions containing hypersurface orthogonal geodesic rays. 11.2. The NUT-Taub metric. 11.3. Type D vacuum metrics -- 12. The Bondi-Metzner-Sachs group. 12.1. The Bondi-Metzner-Sachs group. 12.2. The structure of the Bondi-Metzner-Sachs Group
- Control code
- 827949108
- Dimensions
- unknown
- Extent
- 1 online resource (xviii, 391 pages)
- File format
- unknown
- Form of item
- online
- Isbn
- 9781848160187
- 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
- (OCoLC)827949108
- Label
- Group theory and general relativity : representations of the Lorentz group and their applications to the gravitational field, Moshe Carmeli
- Note
- Originally published: New York : McGraw-Hill, ©1977
- Antecedent source
- unknown
- Bibliography note
- Includes bibliographical references (pages 343-375) 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
- 1. The rotation group. 1.1. The three-dimensional pure rotation group. 1.2. The group SU[symbol]. 1.3. Invariant integral over the groups O[symbol] and SU[symbol]. 1.4. Representations of the groups O[symbol] and SU[symbol]. 1.5. Matrix elements of irreducible representations. 1.6. Differential operators of infinitesimal rotations -- 2. The Lorentz group. 2.1. Infinitesimal Lorentz matrices. 2.2. Infinitesimal Operators. 2.3. Representations of the group L -- 3. Spinor representation of the Lorentz group. 3.1. The group SL(2, C) and the Lorentz group. 3.2. Spinor representation of the group SL(2, C). 3.3. Infinitesimal operators of the spinor representation -- 4. Principal series of representations of SL(2, C). 4.1. Linear spaces of representations. 4.2. The group operators. 4.3. SU[symbol] description of the principal series. 4.4. Comparison with the infinitesimal approach -- 5. Complementary series of representations of SL(2, C). 5.1. Realization of the complementary series. 5.2. SU[symbol] description of the complementary series. 5.3. Operator formulation -- 6. Complete series of representations of SL(2, C). 6.1. Realization of the complete series. 6.2. Complete series and spinors. 6.3. Unitary representations case. 6.4. Harmonic analysis on the group SL(2, C) -- 7. Elements of general relativity theory. 7.1. Riemannian geometry. 7.2. Principle of equivalence. 7.3. Principle of general covariance. 7.4. Gravitational field equations. 7.5. Solutions of Einstein's field equations. 7.6. Experimental tests of general relativity. 7.7. Equations of motion -- 8. Spinors in general relativity. 8.1. Connection between spinors and tensors. 8.2. Maxwell, Weyl and Riemann spinors. 8.3. Classification of Maxwell spinor. 8.4. Classification of Weyl spinor -- 9. SL(2, C) gauge theory of the gravitational field: the Newman-Penrose equations. 9.1. Isotopic spin and gauge fields. 9.2. Lorentz invariance and the gravitational field. 9.3. SL(2, C) invariance and the gravitational field. 9.4. Gravitational field equations -- 10. Analysis of the gravitational field. 10.1. Geometrical interpretation. 10.2. Choice of coordinate system. 10.3. Asymptotic behavior -- 11. Some exact solutions of the gravitational field equations. 11.1. Solutions containing hypersurface orthogonal geodesic rays. 11.2. The NUT-Taub metric. 11.3. Type D vacuum metrics -- 12. The Bondi-Metzner-Sachs group. 12.1. The Bondi-Metzner-Sachs group. 12.2. The structure of the Bondi-Metzner-Sachs Group
- Control code
- 827949108
- Dimensions
- unknown
- Extent
- 1 online resource (xviii, 391 pages)
- File format
- unknown
- Form of item
- online
- Isbn
- 9781848160187
- 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
- (OCoLC)827949108
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