Language:
English
繁體中文
Help
Login
Back
Switch To:
Labeled
|
MARC Mode
|
ISBD
Geometry from Dynamics, Classical an...
~
Ibort, Alberto.
Geometry from Dynamics, Classical and Quantum
Record Type:
Language materials, printed : Monograph/item
Title/Author:
Geometry from Dynamics, Classical and Quantum/ by José F. Cariñena, Alberto Ibort, Giuseppe Marmo, Giuseppe Morandi.
Author:
Cariñena, José F.
other author:
Ibort, Alberto.
Description:
XXV, 719 p. 22 illus.online resource. :
Contained By:
Springer Nature eBook
Subject:
Mathematical physics. -
Online resource:
https://doi.org/10.1007/978-94-017-9220-2
ISBN:
9789401792202
Geometry from Dynamics, Classical and Quantum
Cariñena, José F.
Geometry from Dynamics, Classical and Quantum
[electronic resource] /by José F. Cariñena, Alberto Ibort, Giuseppe Marmo, Giuseppe Morandi. - 1st ed. 2015. - XXV, 719 p. 22 illus.online resource.
Contents -- Foreword -- Some examples of linear and nonlinear physical systems and their dynamical equations -- The language of geometry and dynamical systems: the linearity paradigm -- The geometrization of dynamical systems -- Invariant structures for dynamical systems: Poisson and Jacobi dynamics -- The classical formulations of dynamics of Hamilton and Lagrange -- The geometry of Hermitean spaces: quantum evolution -- Folding and unfolding Classical and Quantum systems -- Integrable and superintegrable systems -- Lie-Scheffers systems -- Appendices -- Bibliography -- Index.
This book describes, by using elementary techniques, how some geometrical structures widely used today in many areas of physics, like symplectic, Poisson, Lagrangian, Hermitian, etc., emerge from dynamics. It is assumed that what can be accessed in actual experiences when studying a given system is just its dynamical behavior that is described by using a family of variables ("observables" of the system). The book departs from the principle that ''dynamics is first'', and then tries to answer in what sense the sole dynamics determines the geometrical structures that have proved so useful to describe the dynamics in so many important instances. In this vein it is shown that most of the geometrical structures that are used in the standard presentations of classical dynamics (Jacobi, Poisson, symplectic, Hamiltonian, Lagrangian) are determined, though in general not uniquely, by the dynamics alone. The same program is accomplished for the geometrical structures relevant to describe quantum dynamics. Finally, it is shown that further properties that allow the explicit description of the dynamics of certain dynamical systems, like integrability and superintegrability, are deeply related to the previous development and will be covered in the last part of the book. The mathematical framework used to present the previous program is kept to an elementary level throughout the text, indicating where more advanced notions will be needed to proceed further. A family of relevant examples is discussed at length and the necessary ideas from geometry are elaborated along the text. However no effort is made to present an ''all-inclusive'' introduction to differential geometry as many other books already exist on the market doing exactly that. However, the development of the previous program, considered as the posing and solution of a generalized inverse problem for geometry, leads to new ways of thinking and relating some of the most conspicuous geometrical structures appearing in Mathematical and Theoretical Physics.
ISBN: 9789401792202
Standard No.: 10.1007/978-94-017-9220-2doiSubjects--Topical Terms:
527831
Mathematical physics.
LC Class. No.: QC19.2-20.85
Dewey Class. No.: 530.1
Geometry from Dynamics, Classical and Quantum
LDR
:03987nam a22003975i 4500
001
966607
003
DE-He213
005
20200702140119.0
007
cr nn 008mamaa
008
201211s2015 ne | s |||| 0|eng d
020
$a
9789401792202
$9
978-94-017-9220-2
024
7
$a
10.1007/978-94-017-9220-2
$2
doi
035
$a
978-94-017-9220-2
050
4
$a
QC19.2-20.85
072
7
$a
PHU
$2
bicssc
072
7
$a
SCI040000
$2
bisacsh
072
7
$a
PHU
$2
thema
082
0 4
$a
530.1
$2
23
100
1
$a
Cariñena, José F.
$e
author.
$4
aut
$4
http://id.loc.gov/vocabulary/relators/aut
$3
1262215
245
1 0
$a
Geometry from Dynamics, Classical and Quantum
$h
[electronic resource] /
$c
by José F. Cariñena, Alberto Ibort, Giuseppe Marmo, Giuseppe Morandi.
250
$a
1st ed. 2015.
264
1
$a
Dordrecht :
$b
Springer Netherlands :
$b
Imprint: Springer,
$c
2015.
300
$a
XXV, 719 p. 22 illus.
$b
online resource.
336
$a
text
$b
txt
$2
rdacontent
337
$a
computer
$b
c
$2
rdamedia
338
$a
online resource
$b
cr
$2
rdacarrier
347
$a
text file
$b
PDF
$2
rda
505
0
$a
Contents -- Foreword -- Some examples of linear and nonlinear physical systems and their dynamical equations -- The language of geometry and dynamical systems: the linearity paradigm -- The geometrization of dynamical systems -- Invariant structures for dynamical systems: Poisson and Jacobi dynamics -- The classical formulations of dynamics of Hamilton and Lagrange -- The geometry of Hermitean spaces: quantum evolution -- Folding and unfolding Classical and Quantum systems -- Integrable and superintegrable systems -- Lie-Scheffers systems -- Appendices -- Bibliography -- Index.
520
$a
This book describes, by using elementary techniques, how some geometrical structures widely used today in many areas of physics, like symplectic, Poisson, Lagrangian, Hermitian, etc., emerge from dynamics. It is assumed that what can be accessed in actual experiences when studying a given system is just its dynamical behavior that is described by using a family of variables ("observables" of the system). The book departs from the principle that ''dynamics is first'', and then tries to answer in what sense the sole dynamics determines the geometrical structures that have proved so useful to describe the dynamics in so many important instances. In this vein it is shown that most of the geometrical structures that are used in the standard presentations of classical dynamics (Jacobi, Poisson, symplectic, Hamiltonian, Lagrangian) are determined, though in general not uniquely, by the dynamics alone. The same program is accomplished for the geometrical structures relevant to describe quantum dynamics. Finally, it is shown that further properties that allow the explicit description of the dynamics of certain dynamical systems, like integrability and superintegrability, are deeply related to the previous development and will be covered in the last part of the book. The mathematical framework used to present the previous program is kept to an elementary level throughout the text, indicating where more advanced notions will be needed to proceed further. A family of relevant examples is discussed at length and the necessary ideas from geometry are elaborated along the text. However no effort is made to present an ''all-inclusive'' introduction to differential geometry as many other books already exist on the market doing exactly that. However, the development of the previous program, considered as the posing and solution of a generalized inverse problem for geometry, leads to new ways of thinking and relating some of the most conspicuous geometrical structures appearing in Mathematical and Theoretical Physics.
650
0
$a
Mathematical physics.
$3
527831
650
0
$a
Statistical physics.
$3
528048
650
0
$a
Dynamical systems.
$3
1249739
650
0
$a
Differential geometry.
$3
882213
650
0
$a
Mechanics.
$3
527684
650
1 4
$a
Theoretical, Mathematical and Computational Physics.
$3
768900
650
2 4
$a
Mathematical Physics.
$3
786661
650
2 4
$a
Complex Systems.
$3
888664
650
2 4
$a
Differential Geometry.
$3
671118
650
2 4
$a
Classical Mechanics.
$3
1140387
650
2 4
$a
Statistical Physics and Dynamical Systems.
$3
1114011
700
1
$a
Ibort, Alberto.
$e
author.
$4
aut
$4
http://id.loc.gov/vocabulary/relators/aut
$3
1262216
700
1
$a
Marmo, Giuseppe.
$4
aut
$4
http://id.loc.gov/vocabulary/relators/aut
$3
672832
700
1
$a
Morandi, Giuseppe.
$e
author.
$4
aut
$4
http://id.loc.gov/vocabulary/relators/aut
$3
1262217
710
2
$a
SpringerLink (Online service)
$3
593884
773
0
$t
Springer Nature eBook
776
0 8
$i
Printed edition:
$z
9789401792219
776
0 8
$i
Printed edition:
$z
9789401792196
776
0 8
$i
Printed edition:
$z
9789402401547
856
4 0
$u
https://doi.org/10.1007/978-94-017-9220-2
912
$a
ZDB-2-PHA
912
$a
ZDB-2-SXP
950
$a
Physics and Astronomy (SpringerNature-11651)
950
$a
Physics and Astronomy (R0) (SpringerNature-43715)
based on 0 review(s)
Multimedia
Reviews
Add a review
and share your thoughts with other readers
Export
pickup library
Processing
...
Change password
Login