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In 1941, E.C.G. Stueckelberg wrote a paper, based on ideas of V.
Fock, that established the foundations of a theory that could
covariantly describe the classical and quantum relativistic
mechanics of a single particle. Horwitz and Piron extended the
applicability of this theory in 1973 (to be called the SHP theory)
to the many-body problem. It is the purpose of this book to explain
this development and provide examples of its applications. We first
review the basic ideas of the SHP theory, both classical and
quantum, and develop the appropriate form of electromagnetism on
this dynamics. After studying the two body problem classically and
quantum mechanically, we formulate the N-body problem. We then
develop the general quantum scattering theory for the N-body
problem and prove a quantum mechanical relativistically covariant
form of the Gell-Mann-Low theorem. The quantum theory of
relativistic spin is then developed, including spin-statistics,
providing the necessary apparatus for Clebsch-Gordan additivity,
and we then discuss the phenomenon of entanglement at unequal
times. In the second part, we develop relativistic statistical
mechanics, including a mechanism for stability of the off-shell
mass, and a high temperature phase transition to the mass shell.
Finally, some applications are given, such as the explanation of
the Lindneret alexperiment, the proposed experiment of Palacios et
al which should demonstrate relativistic entanglement (at unequal
times), the space-time lattice, low energy nuclear reactions and
applications to black hole physics.
In 1941, E.C.G. Stueckelberg wrote a paper, based on ideas of V.
Fock, that established the foundations of a theory that could
covariantly describe the classical and quantum relativistic
mechanics of a single particle. Horwitz and Piron extended the
applicability of this theory in 1973 (to be called the SHP theory)
to the many-body problem. It is the purpose of this book to explain
this development and provide examples of its applications. We first
review the basic ideas of the SHP theory, both classical and
quantum, and develop the appropriate form of electromagnetism on
this dynamics. After studying the two body problem classically and
quantum mechanically, we formulate the N-body problem. We then
develop the general quantum scattering theory for the N-body
problem and prove a quantum mechanical relativistically covariant
form of the Gell-Mann-Low theorem. The quantum theory of
relativistic spin is then developed, including spin-statistics,
providing the necessary apparatus for Clebsch-Gordan additivity,
and we then discuss the phenomenon of entanglement at unequal
times. In the second part, we develop relativistic statistical
mechanics, including a mechanism for stability of the off-shell
mass, and a high temperature phase transition to the mass shell.
Finally, some applications are given, such as the explanation of
the Lindneret alexperiment, the proposed experiment of Palacios et
al which should demonstrate relativistic entanglement (at unequal
times), the space-time lattice, low energy nuclear reactions and
applications to black hole physics.
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