Check nearby libraries
Buy this book
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.
Check nearby libraries
Buy this book
Showing 4 featured editions. View all 4 editions?
Edition | Availability |
---|---|
1
Geometry from Dynamics, Classical and Quantum
Oct 28, 2016, Springer
paperback
9402401547 9789402401547
|
zzzz
Libraries near you:
WorldCat
|
2
Geometry from Dynamics, Classical and Quantum
2014, Springer London, Limited
in English
9401792208 9789401792202
|
aaaa
Libraries near you:
WorldCat
|
3
Geometry from Dynamics, Classical and Quantum
Oct 08, 2014, Springer
hardcover
9401792194 9789401792196
|
zzzz
Libraries near you:
WorldCat
|
4
Geometry from Dynamics, Classical and Quantum
Sep 28, 2014, Springer
paperback
9401792216 9789401792219
|
zzzz
Libraries near you:
WorldCat
|
Book Details
Classifications
The Physical Object
ID Numbers
Community Reviews (0)
Feedback?History
- Created February 26, 2022
- 1 revision
Wikipedia citation
×CloseCopy and paste this code into your Wikipedia page. Need help?
February 26, 2022 | Created by ImportBot | Imported from Better World Books record |