 02101 Yaakov Friedman, Yuriy Gofman
 Relativistic Dynamic Equation in Invariant Form
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Mar 5, 02

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Abstract. In some dynamical systems boosts and
rotations occur synchronically. Usually in analysis of such
systems we separate these two types of motion. Unfortunately, the
result of such analysis depends on the order in which operations
are performed.
To avoid the order dependence of the above operations, we propose
a new dynamic variable called the symmetric velocity. This new
velocity could be calculated directly from the regular velocity
and is its relativistic half. The set of all possible symmetric
velocities is a three dimensional ball of radius \textit{c} and
the Lorentz group acts on this ball via conformal maps. The
generators of these maps (elements of the Lie algebra) are second
order transformations expressed by a triple product. This triple
product is the one corresponding to the Bounded Symmetric Domain
of type 4 in Cartan's classification, also called the spin
factor. The product is connected with the Geometric (Clifford)
product, explaining why use of the geometric product simplifies
formulae in several areas of physics.
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