Bibcode
Hajjawi, S.; Buitrago, J.
Bibliographical reference
Journal of Mathematical Physics, Volume 48, Issue 2, pp. 022902-022902-14 (2007).
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2
2007
Journal
Citations
4
Refereed citations
3
Description
As previously shown, the special relativistic dynamical equation of the
Lorentz force type can be regarded as a consequence of a succession of
space-time dependent infinitesimal Lorentz boosts and rotations. This
insight indicates that the Lorentz-Force-like equation has a fundamental
meaning in physics. We show how this result may be spinorially obtained
starting out from the application of an infinitesimal element of SL(2,C)
to the individual spinors, which are regarded here as being more
fundamental objects than four-vectors. In this way we get a set of new
dynamical spinor equations inducing the extended Lorentz-Force-like
equation in the Minkowski space-time and geometrically obtain the spinor
form of the electromagnetic field tensor. The term extended refers to
the dynamics of some additional degrees of freedom that may be
associated with the intrinsic spin, namely, with the dynamics of three
spacelike mutually orthogonal four-vectors, all of them orthogonal to
the linear four-momentum of the object under consideration that finally,
in the particle's proper frame, are identified with the generators of
SU(2).