Abstract
We derive the laws of superposition of multiple successive collinear
Lorentz boosts by four different methods. The first method exploits the
relation between the Pochhammers of 2x2 nonautonomous matrices and the
symmetric functions. The second method proceeds by diagonalizing the
Lorentz boost. The third method is based on the characteristics of the
Pauli matrices. The fourth method makes use of the relativistic law of
addition of multiple collinear velocities, as well as the polygonometric
identities. We give expressions, for the laws of superposition,
parametrized using velocity and rapidity, as well as expressions in
compact, symmetric and unified forms. We also give the expressions of the
laws of superposition in the special case of identical boosts, both for
finite boosts, and for infinitesimal boosts. These latter results provide
insight into the relation between Galilean (classical) and Lorentzian
(relativistic) velocities.
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