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010 2011280752
019 741492796
020 9789814313728|q(electronic book)
020 9814313726|q(electronic book)
020 9789814313735|q(electronic book)
020 9814313734|q(electronic book)
035 (OCoLC)742413680|z(OCoLC)741492796
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050 4 QC174.17.G46|bG53 2011eb
072 7 SCI|x040000|2bisacsh
082 04 530.155353|222
090 QC174.17.G46|bG53 2011eb
100 1 Giachetta, G.|0https://id.loc.gov/authorities/names/
n98088810
245 10 Geometric formulation of classical and quantum mechanics /
|cGiovanni Giachetta, Luigi Mangiarotti, Gennadi
Sardanashvily.
264 1 Singapore ;|aHackensack, NJ ;|aLondon :|bWorld Scientific,
|c[2011]
264 4 |c©2011
300 1 online resource (xi, 392 pages)
336 text|btxt|2rdacontent
337 computer|bc|2rdamedia
338 online resource|bcr|2rdacarrier
340 |gpolychrome|2rdacc
347 text file|2rdaft
504 Includes bibliographical references (pages 369-376) and
index.
505 0 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 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 Print version record.
590 eBooks on EBSCOhost|bEBSCO eBook Subscription Academic
Collection - North America
650 0 Mechanics|0https://id.loc.gov/authorities/subjects/
sh85082767|xMathematics.|0https://id.loc.gov/authorities/
subjects/sh2002007922
650 0 Quantum theory|xMathematics.|0https://id.loc.gov/
authorities/subjects/sh2008122823
650 0 Geometry, Differential.|0https://id.loc.gov/authorities/
subjects/sh85054146
650 0 Mathematical physics.|0https://id.loc.gov/authorities/
subjects/sh85082129
650 7 Mechanics|xMathematics.|2fast|0https://id.worldcat.org/
fast/1013460
650 7 Mechanics.|2fast|0https://id.worldcat.org/fast/1013446
650 7 Quantum theory|xMathematics.|2fast|0https://
id.worldcat.org/fast/1085135
650 7 Geometry, Differential.|2fast|0https://id.worldcat.org/
fast/940919
650 7 Mathematical physics.|2fast|0https://id.worldcat.org/fast/
1012104
655 0 Electronic books.
655 4 Electronic books.
700 1 Magiaradze, L. G.|0https://id.loc.gov/authorities/names/
n79115151
700 1 Sardanashvili, G. A.|q(Gennadiĭ Aleksandrovich)|0https://
id.loc.gov/authorities/names/n85193388
776 08 |iPrint version:|aGiachetta, G.|tGeometric formulation of
classical and quantum mechanics.|dSingapore ; Hackensack,
NJ ; London : World Scientific, ©2011|z9789814313728
|w(OCoLC)613430950
856 40 |uhttps://rider.idm.oclc.org/login?url=http://
search.ebscohost.com/login.aspx?direct=true&scope=site&
db=nlebk&AN=374879|zOnline eBook. Access restricted to
current Rider University students, faculty, and staff.
856 42 |3Instructions for reading/downloading this eBook|uhttp://
guides.rider.edu/ebooks/ebsco
901 MARCIVE 20231220
948 |d20160616|cEBSCO|tebscoebooksacademic|lridw
994 92|bRID
