The main idea is that, while the energy-momentum is a single four-vector in the dual of the Hermitian
subspace of , the angular momentum is not only an anti-symmetric tensor over the same space,
but should depend on the ‘origin’, a point in a four-dimensional affine space
as well, and should
transform in a specific way under the translation of the ‘origin’. Bergqvist and Ludvigsen defined the affine
space
to be the space of the solutions
of
, and showed that
is, in fact,
a real, four-dimensional affine space. Then, for a given
, to each
-constant spinor field
they associate a primed spinor field by
. This
turns out to satisfy the
modified valence-one twistor equation
. Finally, they form the 2-form
http://www.livingreviews.org/lrr-2009-4 |
Living Rev. Relativity 12, (2009), 4
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