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Books > Science & Mathematics > Mathematics > Geometry > Differential & Riemannian geometry
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Geometry from Dynamics, Classical and Quantum (Paperback, Softcover reprint of the original 1st ed. 2015)
Loot Price: R2,942
Discovery Miles 29 420
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Geometry from Dynamics, Classical and Quantum (Paperback, Softcover reprint of the original 1st ed. 2015)
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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 super integrability, 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.
General
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