Group theory and general relativity: representations of the Lorentz group and their applications to the gravitational field
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| Format: | Elektronisch E-Book |
| Sprache: | English |
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World Scientific
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| Beschreibung: | Originally published: New York : McGraw-Hill, c1977 Includes bibliographical references (p. 343-375) and index 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 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 |
| Beschreibung: | 1 Online-Ressource (xviii, 391 p.) |
| ISBN: | 0070099863 1848160186 1860942342 9780070099869 9781848160187 9781860942341 |
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| 100 | 1 | |a Carmeli, Moshe |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Group theory and general relativity |b representations of the Lorentz group and their applications to the gravitational field |c Moshe Carmeli |
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| 500 | |a Originally published: New York : McGraw-Hill, c1977 | ||
| 500 | |a Includes bibliographical references (p. 343-375) and index | ||
| 500 | |a 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 -- | ||
| 500 | |a - 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 -- | ||
| 500 | |a - 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 | ||
| 500 | |a 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 | ||
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Datensatz im Suchindex
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| any_adam_object | |
| author | Carmeli, Moshe |
| author_facet | Carmeli, Moshe |
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| author_sort | Carmeli, Moshe |
| author_variant | m c mc |
| building | Verbundindex |
| bvnumber | BV043154815 |
| collection | ZDB-4-EBA |
| ctrlnum | (OCoLC)827949108 (DE-599)BVBBV043154815 |
| dewey-full | 530.11/01/5122 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 530 - Physics |
| dewey-raw | 530.11/01/5122 |
| dewey-search | 530.11/01/5122 |
| dewey-sort | 3530.11 11 45122 |
| dewey-tens | 530 - Physics |
| discipline | Physik |
| format | Electronic eBook |
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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 -- </subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a"> - 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 -- </subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a"> - 9. 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| id | DE-604.BV043154815 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:19:09Z |
| institution | BVB |
| isbn | 0070099863 1848160186 1860942342 9780070099869 9781848160187 9781860942341 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-028579006 |
| oclc_num | 827949108 |
| open_access_boolean | |
| owner | DE-1046 DE-1047 |
| owner_facet | DE-1046 DE-1047 |
| physical | 1 Online-Ressource (xviii, 391 p.) |
| psigel | ZDB-4-EBA ZDB-4-EBA FAW_PDA_EBA |
| publishDate | 2000 |
| publishDateSearch | 2000 |
| publishDateSort | 2000 |
| publisher | World Scientific |
| record_format | marc |
| spelling | Carmeli, Moshe Verfasser aut Group theory and general relativity representations of the Lorentz group and their applications to the gravitational field Moshe Carmeli Singapore World Scientific c2000 1 Online-Ressource (xviii, 391 p.) txt rdacontent c rdamedia cr rdacarrier Originally published: New York : McGraw-Hill, c1977 Includes bibliographical references (p. 343-375) and index 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 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 Darstellung <Mathematik> swd Anwendung swd Gravitationsfeld swd Allgemeine Relativitätstheorie swd Gruppentheorie swd Lorentz-Gruppe swd SCIENCE / Physics / Relativity bisacsh Lorentz transformations fast Lorentz transformations Gravitationsfeld (DE-588)4072014-7 gnd rswk-swf Darstellung Mathematik (DE-588)4128289-9 gnd rswk-swf Lorentz-Gruppe (DE-588)4036335-1 gnd rswk-swf Physik (DE-588)4045956-1 gnd rswk-swf Relativitätstheorie (DE-588)4049363-5 gnd rswk-swf Allgemeine Relativitätstheorie (DE-588)4112491-1 gnd rswk-swf Gruppentheorie (DE-588)4072157-7 gnd rswk-swf Allgemeine Relativitätstheorie (DE-588)4112491-1 s Gruppentheorie (DE-588)4072157-7 s 1\p DE-604 Lorentz-Gruppe (DE-588)4036335-1 s Gravitationsfeld (DE-588)4072014-7 s 2\p DE-604 Darstellung Mathematik (DE-588)4128289-9 s 3\p DE-604 Relativitätstheorie (DE-588)4049363-5 s 4\p DE-604 Physik (DE-588)4045956-1 s 5\p DE-604 http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=516692 Aggregator Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 4\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 5\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Carmeli, Moshe Group theory and general relativity representations of the Lorentz group and their applications to the gravitational field Darstellung <Mathematik> swd Anwendung swd Gravitationsfeld swd Allgemeine Relativitätstheorie swd Gruppentheorie swd Lorentz-Gruppe swd SCIENCE / Physics / Relativity bisacsh Lorentz transformations fast Lorentz transformations Gravitationsfeld (DE-588)4072014-7 gnd Darstellung Mathematik (DE-588)4128289-9 gnd Lorentz-Gruppe (DE-588)4036335-1 gnd Physik (DE-588)4045956-1 gnd Relativitätstheorie (DE-588)4049363-5 gnd Allgemeine Relativitätstheorie (DE-588)4112491-1 gnd Gruppentheorie (DE-588)4072157-7 gnd |
| subject_GND | (DE-588)4072014-7 (DE-588)4128289-9 (DE-588)4036335-1 (DE-588)4045956-1 (DE-588)4049363-5 (DE-588)4112491-1 (DE-588)4072157-7 |
| title | Group theory and general relativity representations of the Lorentz group and their applications to the gravitational field |
| title_auth | Group theory and general relativity representations of the Lorentz group and their applications to the gravitational field |
| title_exact_search | Group theory and general relativity representations of the Lorentz group and their applications to the gravitational field |
| title_full | Group theory and general relativity representations of the Lorentz group and their applications to the gravitational field Moshe Carmeli |
| title_fullStr | Group theory and general relativity representations of the Lorentz group and their applications to the gravitational field Moshe Carmeli |
| title_full_unstemmed | Group theory and general relativity representations of the Lorentz group and their applications to the gravitational field Moshe Carmeli |
| title_short | Group theory and general relativity |
| title_sort | group theory and general relativity representations of the lorentz group and their applications to the gravitational field |
| title_sub | representations of the Lorentz group and their applications to the gravitational field |
| topic | Darstellung <Mathematik> swd Anwendung swd Gravitationsfeld swd Allgemeine Relativitätstheorie swd Gruppentheorie swd Lorentz-Gruppe swd SCIENCE / Physics / Relativity bisacsh Lorentz transformations fast Lorentz transformations Gravitationsfeld (DE-588)4072014-7 gnd Darstellung Mathematik (DE-588)4128289-9 gnd Lorentz-Gruppe (DE-588)4036335-1 gnd Physik (DE-588)4045956-1 gnd Relativitätstheorie (DE-588)4049363-5 gnd Allgemeine Relativitätstheorie (DE-588)4112491-1 gnd Gruppentheorie (DE-588)4072157-7 gnd |
| topic_facet | Darstellung <Mathematik> Anwendung Gravitationsfeld Allgemeine Relativitätstheorie Gruppentheorie Lorentz-Gruppe SCIENCE / Physics / Relativity Lorentz transformations Darstellung Mathematik Physik Relativitätstheorie |
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| work_keys_str_mv | AT carmelimoshe grouptheoryandgeneralrelativityrepresentationsofthelorentzgroupandtheirapplicationstothegravitationalfield |