Geometric formulation of classical and quantum mechanics:
Gespeichert in:
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Singapore
World Scientific
c2011
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| Schlagworte: | |
| Online-Zugang: | FAW01 FAW02 Volltext |
| Beschreibung: | Includes bibliographical references (p. 369-376) and index 1. Dynamic equations. 1.1. Preliminary. Fibre bundles over R. 1.2. Autonomous dynamic equations. 1.3. Dynamic equations. 1.4. Dynamic connections. 1.5. Non-relativistic geodesic equations. 1.6. Reference frames. 1.7. Free motion equations. 1.8. Relative acceleration. 1.9. Newtonian systems. 1.10. Integrals of motion -- 2. Lagrangian mechanics. 2.1. Lagrangian formalism on Q[symbol]R. 2.2. Cartan and Hamilton-De Donder equations. 2.3. Quadratic Lagrangians. 2.4. Lagrangian and Newtonian systems. 2.5. Lagrangian conservation laws. 2.6. Gauge symmetries -- 3. Hamiltonian mechanics. 3.1. Geometry of Poisson manifolds. 3.2. Autonomous Hamiltonian systems. 3.3. Hamiltonian formalism on Q[symbol]R. 3.4. Homogeneous Hamiltonian formalism. 3.5. Lagrangian form of Hamiltonian formalism. 3.6. Associated Lagrangian and Hamiltonian systems. 3.7. Quadratic Lagrangian and Hamiltonian systems. 3.8. Hamiltonian conservation laws. 3.9. Time-reparametrized mechanics -- - 4. Algebraic quantization. 4.1. GNS construction. 4.2. Automorphisms of quantum systems. 4.3. Banach and Hilbert manifolds. 4.4. Hilbert and C*-algebra bundles. 4.5. Connections on Hilbert and C*-algebra bundles. 4.6. Instantwise quantization -- 5. Geometric quantization. 5.1. Geometric quantization of symplectic manifolds. 5.2. Geometric quantization of a cotangent bundle. 5.3. Leafwise geometric quantization. 5.4. Quantization of non-relativistic mechanics. 5.5. Quantization with respect to different reference frames -- 6. Constraint Hamiltonian systems. 6.1. Autonomous Hamiltonian systems with constraints. 6.2. Dirac constraints. 6.3. Time-dependent constraints. 6.4. Lagrangian constraints. 6.5. Geometric quantization of constraint systems -- - 7. Integrable Hamiltonian systems. 7.1. Partially integrable systems with non-compact invariant submanifolds. 7.2. KAM theorem for partially integrable systems. 7.3. Superintegrable systems with non-compact invariant submanifolds. 7.4. Globally superintegrable systems. 7.5. Superintegrable Hamiltonian systems. 7.6. Example. Global Kepler system. 7.7. Non-autonomous integrable systems. 7.8. Quantization of superintegrable systems -- 8. Jacobi fields. 8.1. The vertical extension of Lagrangian mechanics. 8.2. The vertical extension of Hamiltonian mechanics. 8.3. Jacobi fields of completely integrable systems -- 9. Mechanics with time-dependent parameters. 9.1. Lagrangian mechanics with parameters. 9.2. Hamiltonian mechanics with parameters. 9.3. Quantum mechanics with classical parameters. 9.4. Berry geometric factor. 9.5. Non-adiabatic holonomy operator -- - 10. Relativistic mechanics. 10.1. Jets of submanifolds. 10.2. Lagrangian relativistic mechanics. 10.3. Relativistic geodesic equations. 10.4. Hamiltonian relativistic mechanics. 10.5. Geometric quantization of relativistic mechanics The geometric formulation of autonomous Hamiltonian mechanics in the terms of symplectic and Poisson manifolds is generally accepted. The literature on this subject is extensive. The present book provides the geometric formulation of non-autonomous mechanics in a general setting of time-dependent coordinate and reference frame transformations. This formulation of mechanics as like as that of classical field theory lies in the framework of general theory of dynamic systems, and Lagrangian and Hamiltonian formalisms on fiber bundles. The reader will find a strict mathematical exposition of non-autonomous dynamic systems, Lagrangian and Hamiltonian non-relativistic mechanics, relativistic mechanics, quantum non-autonomous mechanics, together with a number of advanced models - superintegrable systems, non-autonomous constrained systems and theory of Jacobi fields. It also contains information on mechanical systems with time-dependent parameters, non-adiabatic Berry phase theory, instantwise quantization, and quantization relative to different reference frames |
| Beschreibung: | 1 Online-Ressource (xi, 392 p.) |
| ISBN: | 9789814313728 9789814313735 9814313726 9814313734 |
Internformat
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| 100 | 1 | |a Giachetta, G. |d 1961-2014 |e Verfasser |0 (DE-588)1192332954 |4 aut | |
| 245 | 1 | 0 | |a Geometric formulation of classical and quantum mechanics |c Giovanni Giachetta, Luigi Mangiarotti, Gennadi Sardanashvily |
| 264 | 1 | |a Singapore |b World Scientific |c c2011 | |
| 300 | |a 1 Online-Ressource (xi, 392 p.) | ||
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| 500 | |a Includes bibliographical references (p. 369-376) and index | ||
| 500 | |a 1. Dynamic equations. 1.1. Preliminary. Fibre bundles over R. 1.2. Autonomous dynamic equations. 1.3. Dynamic equations. 1.4. Dynamic connections. 1.5. Non-relativistic geodesic equations. 1.6. Reference frames. 1.7. Free motion equations. 1.8. Relative acceleration. 1.9. Newtonian systems. 1.10. Integrals of motion -- 2. Lagrangian mechanics. 2.1. Lagrangian formalism on Q[symbol]R. 2.2. Cartan and Hamilton-De Donder equations. 2.3. Quadratic Lagrangians. 2.4. Lagrangian and Newtonian systems. 2.5. Lagrangian conservation laws. 2.6. Gauge symmetries -- 3. Hamiltonian mechanics. 3.1. Geometry of Poisson manifolds. 3.2. Autonomous Hamiltonian systems. 3.3. Hamiltonian formalism on Q[symbol]R. 3.4. Homogeneous Hamiltonian formalism. 3.5. Lagrangian form of Hamiltonian formalism. 3.6. Associated Lagrangian and Hamiltonian systems. 3.7. Quadratic Lagrangian and Hamiltonian systems. 3.8. Hamiltonian conservation laws. 3.9. Time-reparametrized mechanics -- | ||
| 500 | |a - 4. Algebraic quantization. 4.1. GNS construction. 4.2. Automorphisms of quantum systems. 4.3. Banach and Hilbert manifolds. 4.4. Hilbert and C*-algebra bundles. 4.5. Connections on Hilbert and C*-algebra bundles. 4.6. Instantwise quantization -- 5. Geometric quantization. 5.1. Geometric quantization of symplectic manifolds. 5.2. Geometric quantization of a cotangent bundle. 5.3. Leafwise geometric quantization. 5.4. Quantization of non-relativistic mechanics. 5.5. Quantization with respect to different reference frames -- 6. Constraint Hamiltonian systems. 6.1. Autonomous Hamiltonian systems with constraints. 6.2. Dirac constraints. 6.3. Time-dependent constraints. 6.4. Lagrangian constraints. 6.5. Geometric quantization of constraint systems -- | ||
| 500 | |a - 7. Integrable Hamiltonian systems. 7.1. Partially integrable systems with non-compact invariant submanifolds. 7.2. KAM theorem for partially integrable systems. 7.3. Superintegrable systems with non-compact invariant submanifolds. 7.4. Globally superintegrable systems. 7.5. Superintegrable Hamiltonian systems. 7.6. Example. Global Kepler system. 7.7. Non-autonomous integrable systems. 7.8. Quantization of superintegrable systems -- 8. Jacobi fields. 8.1. The vertical extension of Lagrangian mechanics. 8.2. The vertical extension of Hamiltonian mechanics. 8.3. Jacobi fields of completely integrable systems -- 9. Mechanics with time-dependent parameters. 9.1. Lagrangian mechanics with parameters. 9.2. Hamiltonian mechanics with parameters. 9.3. Quantum mechanics with classical parameters. 9.4. Berry geometric factor. 9.5. Non-adiabatic holonomy operator -- | ||
| 500 | |a - 10. Relativistic mechanics. 10.1. Jets of submanifolds. 10.2. Lagrangian relativistic mechanics. 10.3. Relativistic geodesic equations. 10.4. Hamiltonian relativistic mechanics. 10.5. Geometric quantization of relativistic mechanics | ||
| 500 | |a The geometric formulation of autonomous Hamiltonian mechanics in the terms of symplectic and Poisson manifolds is generally accepted. The literature on this subject is extensive. The present book provides the geometric formulation of non-autonomous mechanics in a general setting of time-dependent coordinate and reference frame transformations. This formulation of mechanics as like as that of classical field theory lies in the framework of general theory of dynamic systems, and Lagrangian and Hamiltonian formalisms on fiber bundles. The reader will find a strict mathematical exposition of non-autonomous dynamic systems, Lagrangian and Hamiltonian non-relativistic mechanics, relativistic mechanics, quantum non-autonomous mechanics, together with a number of advanced models - superintegrable systems, non-autonomous constrained systems and theory of Jacobi fields. It also contains information on mechanical systems with time-dependent parameters, non-adiabatic Berry phase theory, instantwise quantization, and quantization relative to different reference frames | ||
| 650 | 7 | |a SCIENCE / Physics / Mathematical & Computational |2 bisacsh | |
| 650 | 4 | |a Mathematik | |
| 650 | 4 | |a Mathematische Physik | |
| 650 | 4 | |a Quantentheorie | |
| 650 | 4 | |a Mechanics |x Mathematics | |
| 650 | 4 | |a Quantum theory |x Mathematics | |
| 650 | 4 | |a Geometry, Differential | |
| 650 | 4 | |a Mathematical physics | |
| 700 | 1 | |a Magiaradze, L. G. |e Sonstige |4 oth | |
| 700 | 1 | |a Sardanašvili, Gennadij A. |d 1950- |e Sonstige |0 (DE-588)14187810X |4 oth | |
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Datensatz im Suchindex
| _version_ | 1804175475079118848 |
|---|---|
| any_adam_object | |
| author | Giachetta, G. 1961-2014 |
| author_GND | (DE-588)1192332954 (DE-588)14187810X |
| author_facet | Giachetta, G. 1961-2014 |
| author_role | aut |
| author_sort | Giachetta, G. 1961-2014 |
| author_variant | g g gg |
| building | Verbundindex |
| bvnumber | BV043082072 |
| collection | ZDB-4-EBA |
| ctrlnum | (OCoLC)742413680 (DE-599)BVBBV043082072 |
| dewey-full | 530.155353 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 530 - Physics |
| dewey-raw | 530.155353 |
| dewey-search | 530.155353 |
| dewey-sort | 3530.155353 |
| dewey-tens | 530 - Physics |
| discipline | Physik |
| format | Electronic eBook |
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| id | DE-604.BV043082072 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:16:52Z |
| institution | BVB |
| isbn | 9789814313728 9789814313735 9814313726 9814313734 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-028506263 |
| oclc_num | 742413680 |
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| owner | DE-1046 DE-1047 |
| owner_facet | DE-1046 DE-1047 |
| physical | 1 Online-Ressource (xi, 392 p.) |
| psigel | ZDB-4-EBA ZDB-4-EBA FAW_PDA_EBA |
| publishDate | 2011 |
| publishDateSearch | 2011 |
| publishDateSort | 2011 |
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| spelling | Giachetta, G. 1961-2014 Verfasser (DE-588)1192332954 aut Geometric formulation of classical and quantum mechanics Giovanni Giachetta, Luigi Mangiarotti, Gennadi Sardanashvily Singapore World Scientific c2011 1 Online-Ressource (xi, 392 p.) txt rdacontent c rdamedia cr rdacarrier Includes bibliographical references (p. 369-376) and index 1. Dynamic equations. 1.1. Preliminary. Fibre bundles over R. 1.2. Autonomous dynamic equations. 1.3. Dynamic equations. 1.4. Dynamic connections. 1.5. Non-relativistic geodesic equations. 1.6. Reference frames. 1.7. Free motion equations. 1.8. Relative acceleration. 1.9. Newtonian systems. 1.10. Integrals of motion -- 2. Lagrangian mechanics. 2.1. Lagrangian formalism on Q[symbol]R. 2.2. Cartan and Hamilton-De Donder equations. 2.3. Quadratic Lagrangians. 2.4. Lagrangian and Newtonian systems. 2.5. Lagrangian conservation laws. 2.6. Gauge symmetries -- 3. Hamiltonian mechanics. 3.1. Geometry of Poisson manifolds. 3.2. Autonomous Hamiltonian systems. 3.3. Hamiltonian formalism on Q[symbol]R. 3.4. Homogeneous Hamiltonian formalism. 3.5. Lagrangian form of Hamiltonian formalism. 3.6. Associated Lagrangian and Hamiltonian systems. 3.7. Quadratic Lagrangian and Hamiltonian systems. 3.8. Hamiltonian conservation laws. 3.9. Time-reparametrized mechanics -- - 4. Algebraic quantization. 4.1. GNS construction. 4.2. Automorphisms of quantum systems. 4.3. Banach and Hilbert manifolds. 4.4. Hilbert and C*-algebra bundles. 4.5. Connections on Hilbert and C*-algebra bundles. 4.6. Instantwise quantization -- 5. Geometric quantization. 5.1. Geometric quantization of symplectic manifolds. 5.2. Geometric quantization of a cotangent bundle. 5.3. Leafwise geometric quantization. 5.4. Quantization of non-relativistic mechanics. 5.5. Quantization with respect to different reference frames -- 6. Constraint Hamiltonian systems. 6.1. Autonomous Hamiltonian systems with constraints. 6.2. Dirac constraints. 6.3. Time-dependent constraints. 6.4. Lagrangian constraints. 6.5. Geometric quantization of constraint systems -- - 7. Integrable Hamiltonian systems. 7.1. Partially integrable systems with non-compact invariant submanifolds. 7.2. KAM theorem for partially integrable systems. 7.3. Superintegrable systems with non-compact invariant submanifolds. 7.4. Globally superintegrable systems. 7.5. Superintegrable Hamiltonian systems. 7.6. Example. Global Kepler system. 7.7. Non-autonomous integrable systems. 7.8. Quantization of superintegrable systems -- 8. Jacobi fields. 8.1. The vertical extension of Lagrangian mechanics. 8.2. The vertical extension of Hamiltonian mechanics. 8.3. Jacobi fields of completely integrable systems -- 9. Mechanics with time-dependent parameters. 9.1. Lagrangian mechanics with parameters. 9.2. Hamiltonian mechanics with parameters. 9.3. Quantum mechanics with classical parameters. 9.4. Berry geometric factor. 9.5. Non-adiabatic holonomy operator -- - 10. Relativistic mechanics. 10.1. Jets of submanifolds. 10.2. Lagrangian relativistic mechanics. 10.3. Relativistic geodesic equations. 10.4. Hamiltonian relativistic mechanics. 10.5. Geometric quantization of relativistic mechanics The geometric formulation of autonomous Hamiltonian mechanics in the terms of symplectic and Poisson manifolds is generally accepted. The literature on this subject is extensive. The present book provides the geometric formulation of non-autonomous mechanics in a general setting of time-dependent coordinate and reference frame transformations. This formulation of mechanics as like as that of classical field theory lies in the framework of general theory of dynamic systems, and Lagrangian and Hamiltonian formalisms on fiber bundles. The reader will find a strict mathematical exposition of non-autonomous dynamic systems, Lagrangian and Hamiltonian non-relativistic mechanics, relativistic mechanics, quantum non-autonomous mechanics, together with a number of advanced models - superintegrable systems, non-autonomous constrained systems and theory of Jacobi fields. It also contains information on mechanical systems with time-dependent parameters, non-adiabatic Berry phase theory, instantwise quantization, and quantization relative to different reference frames SCIENCE / Physics / Mathematical & Computational bisacsh Mathematik Mathematische Physik Quantentheorie Mechanics Mathematics Quantum theory Mathematics Geometry, Differential Mathematical physics Magiaradze, L. G. Sonstige oth Sardanašvili, Gennadij A. 1950- Sonstige (DE-588)14187810X oth http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=374879 Aggregator Volltext |
| spellingShingle | Giachetta, G. 1961-2014 Geometric formulation of classical and quantum mechanics SCIENCE / Physics / Mathematical & Computational bisacsh Mathematik Mathematische Physik Quantentheorie Mechanics Mathematics Quantum theory Mathematics Geometry, Differential Mathematical physics |
| title | Geometric formulation of classical and quantum mechanics |
| title_auth | Geometric formulation of classical and quantum mechanics |
| title_exact_search | Geometric formulation of classical and quantum mechanics |
| title_full | Geometric formulation of classical and quantum mechanics Giovanni Giachetta, Luigi Mangiarotti, Gennadi Sardanashvily |
| title_fullStr | Geometric formulation of classical and quantum mechanics Giovanni Giachetta, Luigi Mangiarotti, Gennadi Sardanashvily |
| title_full_unstemmed | Geometric formulation of classical and quantum mechanics Giovanni Giachetta, Luigi Mangiarotti, Gennadi Sardanashvily |
| title_short | Geometric formulation of classical and quantum mechanics |
| title_sort | geometric formulation of classical and quantum mechanics |
| topic | SCIENCE / Physics / Mathematical & Computational bisacsh Mathematik Mathematische Physik Quantentheorie Mechanics Mathematics Quantum theory Mathematics Geometry, Differential Mathematical physics |
| topic_facet | SCIENCE / Physics / Mathematical & Computational Mathematik Mathematische Physik Quantentheorie Mechanics Mathematics Quantum theory Mathematics Geometry, Differential Mathematical physics |
| url | http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=374879 |
| work_keys_str_mv | AT giachettag geometricformulationofclassicalandquantummechanics AT magiaradzelg geometricformulationofclassicalandquantummechanics AT sardanasviligennadija geometricformulationofclassicalandquantummechanics |