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This book deals with underlying basic concepts in relativity. The
fundamental work of Stueckelberg, who formulated a consistent
relativistic classical and quantum dynamics, generalized for
application to many-body systems by Horwitz and Piron (SHP theory),
is explained with emphasis on its conceptual content. The two-body
bound state and scattering theory are also discussed. The ideas are
involved in the Lindner experiment showing interference in time and
the proposed experiment of Palacios et al. searching for the
persistence of entanglement at unequal times is discussed. The
meaning of the Newton-Wigner position operator and the
Landau-Peierls construction in terms of relativistic dynamics is
given. Finally, the embedding of the SHP theory into the framework
of general relativity, providing a canonical structure with
particle coordinates and momenta, is studied, carrying with it new
concepts in relativistic dynamics.
This book focuses on unstable systems both from the classical and
the quantum mechanical points of view and studies the relations
between them. The first part deals with quantum systems. Here the
main generally used methods today, such as the Gamow approach, and
the Wigner-Weisskopf method, are critically discussed. The quantum
mechanical Lax-Phillips theory developed by the authors, based on
the dilation theory of Nagy and Foias and its more general
extension to approximate semigroup evolution is explained. The
second part provides a description of approaches to classical
stability analysis and introduces geometrical methods recently
developed by the authors, which are shown to be highly effective in
diagnosing instability and, in many cases, chaotic behavior. It is
then shown that, in the framework of the theory of symplectic
manifolds, there is a systematic algorithm for the construction of
a canonical transformation of any standard potential model
Hamiltonian to geometric form, making accessible powerful geometric
methods for stability analysis in a wide range of applications.
This book focuses on unstable systems both from the classical and
the quantum mechanical points of view and studies the relations
between them. The first part deals with quantum systems. Here the
main generally used methods today, such as the Gamow approach, and
the Wigner-Weisskopf method, are critically discussed. The quantum
mechanical Lax-Phillips theory developed by the authors, based on
the dilation theory of Nagy and Foias and its more general
extension to approximate semigroup evolution is explained. The
second part provides a description of approaches to classical
stability analysis and introduces geometrical methods recently
developed by the authors, which are shown to be highly effective in
diagnosing instability and, in many cases, chaotic behavior. It is
then shown that, in the framework of the theory of symplectic
manifolds, there is a systematic algorithm for the construction of
a canonical transformation of any standard potential model
Hamiltonian to geometric form, making accessible powerful geometric
methods for stability analysis in a wide range of applications.
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