Cargando…
Geometric formulation of classical and quantum 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 co...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Otros Autores: | , |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Singapore ; Hackensack, NJ ; London :
World Scientific,
©2011.
|
| Temas: | |
| Acceso en línea: | Texto completo |
MARC
| LEADER | 00000cam a2200000 a 4500 | ||
|---|---|---|---|
| 001 | EBSCO_ocn742413680 | ||
| 003 | OCoLC | ||
| 005 | 20231017213018.0 | ||
| 006 | m o d | ||
| 007 | cr cnu---unuuu | ||
| 008 | 110725s2011 si ob 001 0 eng d | ||
| 040 | |a N$T |b eng |e pn |c N$T |d E7B |d STF |d OCLCQ |d DEBSZ |d OCLCQ |d YDXCP |d OCLCO |d OCLCQ |d NLGGC |d EBLCP |d WAU |d OCLCQ |d OCLCO |d OCLCF |d OCLCO |d OCLCQ |d OCLCO |d AZK |d LOA |d COCUF |d AGLDB |d MOR |d PIFAG |d VGM |d ZCU |d MERUC |d OCLCQ |d JBG |d OCLCQ |d U3W |d WRM |d OCLCQ |d VTS |d NRAMU |d CRU |d OCLCQ |d INT |d VT2 |d OCLCQ |d WYU |d TKN |d OCLCQ |d LEAUB |d DKC |d OCLCQ |d AJS |d OCLCQ |d OCLCO |d OCLCQ |d OCLCO | ||
| 016 | 7 | |a 015655413 |2 Uk | |
| 019 | |a 741492796 |a 961543481 |a 962587056 | ||
| 020 | |a 9789814313728 |q (electronic bk.) | ||
| 020 | |a 9814313726 |q (electronic bk.) | ||
| 020 | |a 9789814313735 |q (electronic bk.) | ||
| 020 | |a 9814313734 |q (electronic bk.) | ||
| 029 | 1 | |a AU@ |b 000047752790 | |
| 029 | 1 | |a AU@ |b 000048829177 | |
| 029 | 1 | |a AU@ |b 000051582492 | |
| 029 | 1 | |a DEBBG |b BV043082072 | |
| 029 | 1 | |a DEBBG |b BV044156190 | |
| 029 | 1 | |a DEBSZ |b 372878911 | |
| 029 | 1 | |a DEBSZ |b 379321491 | |
| 029 | 1 | |a DEBSZ |b 421583819 | |
| 029 | 1 | |a DEBSZ |b 454995644 | |
| 029 | 1 | |a HEBIS |b 286064685 | |
| 029 | 1 | |a NZ1 |b 14167681 | |
| 035 | |a (OCoLC)742413680 |z (OCoLC)741492796 |z (OCoLC)961543481 |z (OCoLC)962587056 | ||
| 050 | 4 | |a QC174.17.G46 |b G53 2011eb | |
| 072 | 7 | |a SCI |x 040000 |2 bisacsh | |
| 082 | 0 | 4 | |a 530.155353 |2 22 |
| 049 | |a UAMI | ||
| 100 | 1 | |a Giachetta, G. | |
| 245 | 1 | 0 | |a Geometric formulation of classical and quantum mechanics / |c Giovanni Giachetta, Luigi Mangiarotti, Gennadi Sardanashvily. |
| 260 | |a Singapore ; |a Hackensack, NJ ; |a London : |b World Scientific, |c ©2011. | ||
| 300 | |a 1 online resource (xi, 392 pages) | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 347 | |a data file | ||
| 504 | |a Includes bibliographical references (pages 369-376) and index. | ||
| 505 | 0 | |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 -- 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. | |
| 520 | |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. | ||
| 588 | 0 | |a Print version record. | |
| 590 | |a eBooks on EBSCOhost |b EBSCO eBook Subscription Academic Collection - Worldwide | ||
| 650 | 0 | |a Mechanics |x Mathematics. | |
| 650 | 0 | |a Quantum theory |x Mathematics. | |
| 650 | 0 | |a Geometry, Differential. | |
| 650 | 0 | |a Mathematical physics. | |
| 650 | 6 | |a Mécanique |x Mathématiques. | |
| 650 | 6 | |a Théorie quantique |x Mathématiques. | |
| 650 | 6 | |a Géométrie différentielle. | |
| 650 | 6 | |a Physique mathématique. | |
| 650 | 7 | |a SCIENCE |x Physics |x Mathematical & Computational. |2 bisacsh | |
| 650 | 7 | |a Geometry, Differential |2 fast | |
| 650 | 7 | |a Mathematical physics |2 fast | |
| 650 | 7 | |a Mechanics |x Mathematics |2 fast | |
| 650 | 7 | |a Quantum theory |x Mathematics |2 fast | |
| 700 | 1 | |a Magiaradze, L. G. | |
| 700 | 1 | |a Sardanashvili, G. A. |q (Gennadiĭ Aleksandrovich) | |
| 776 | 0 | 8 | |i Print version: |a Giachetta, G. |t Geometric formulation of classical and quantum mechanics. |d Singapore ; Hackensack, NJ ; London : World Scientific, ©2011 |z 9789814313728 |w (OCoLC)613430950 |
| 856 | 4 | 0 | |u https://ebsco.uam.elogim.com/login.aspx?direct=true&scope=site&db=nlebk&AN=374879 |z Texto completo |
| 938 | |a EBL - Ebook Library |b EBLB |n EBL731099 | ||
| 938 | |a ebrary |b EBRY |n ebr10480121 | ||
| 938 | |a EBSCOhost |b EBSC |n 374879 | ||
| 938 | |a YBP Library Services |b YANK |n 6965125 | ||
| 994 | |a 92 |b IZTAP | ||