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Lorentz invariant relative velocity and relativistic binary collisions
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This article reviews the concept of Lorentz invariant relative velocity that is often misunderstood or unknown in high energy physics literature. The properties of the relative velocity allow to formulate the invariant flux and cross section without recurring to non--physical velocities or any assumption about the reference frame. Applications such as the luminosity of a collider, the use as kinematic variable, and the statistical theory of collisions in a relativistic classical gas are reviewed. It is emphasized how the hyperbolic properties of the velocity space explain the peculiarities of relativistic scattering.
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Defining of three-dimensional acceleration and inertial mass leading to the simple form F=MA of relativistic motion equation
A new definition of relativistic acceleration A makes the relativistic equation of motion take the simple form F = M A with M = mγ, unifying longitudinal and transverse mass.
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